My theory, at least what I've had for a while:

Jin before becoming a psycho was actually a person who sought to do good. Reason why he was student council president, model student and a great soldier. However those achievements were always very shallow for him, he never felt he was doing something truly good for others, helping in an important way.

From childhood he actually got along with both Ragna and Saya at the beginning, but something must have happened between him and Saya, something particular from this timeline, my guess is that Saya knew she was something special or Jin's power of Order was different this timeline, perhaps more powerful than any of his past incarnations (because if it was the same as other loops why would Rachel take interest in him when Hakumen is around?), this led to a certain "betrayal" from Saya making Jin "hate" her and cling to Ragna, the family situation got worse by then.

Even after the church incident Jin held his brothers dearly, due to Terumi eating his memories he no longer remembered the church incident exactly, but the feelings inside remained: Ragna ditched him, Saya didn't get along and the duodecim looked down on him, with this he began in a circle of self-depreciation and fear from others, which translates into his cold personality to avoid people but also his willingness to give his best at everything in order to be of help, somehow, do the better thing with so much damage from him in his past.

This is why he asks Saya if she will come back. The extreme of the things he, more than despise, sees as failures of how things have gone wrong in his life can be fixed, if he can actually become someone who can earn something to be happy and do something for others.

In the darkness of the wasteland,
... the vastness surrounds you
Saya, will you return to me?

Nothing in sight, everything seems wrong, no hope, can things be fixed?

It was Sanctuary...
... with no hope of ever escaping,
What remains is still more precious now.

His life was happy, good times, bad times, he couldn't change things when they were ruined, but he holds dear the good memories even after these were stained by dark times.

But from where you are
... you can see a thousand wolds below...
... a thousand different suns everyday...

Saya is special, she can see, understand things nobody else can, something Jin will never hope to understand himself and much less feel, that's why they had grown distant.

I can feel you near,
... helping me to see beyond the walls,
Please, strengthen my resolve.

Saya has given him her legacy: Yukianesa, the sword reminds him of her, gives him a newfound power, Jin feels this, believes this gift will give him a chance and hopes the blade will accompany him in his quest.

For I... I must choose the path before me
As protector, sworn and true,
Steadfastly watching o'er the world,
Fate has death me the jokers and kings,
A hand I cannot refuse.
Ready to fight.
Forever... Alone

His mission is not clear, he wants to do what's right, but doesn't find an answer, all he can do is see the harm in the world, being weak and powerless to do anything to solve it, but he knows he must do something, he has done too much harm in the past and knows esccaping is not an option, he has the resolve and knows that for all his faults he will not be helped in this ordeal, this is his fight and his alone.

There are places I've been to
... but no one I know there
Ikaruga left its vicious mark

Over and over he sees guilt, but Ikaruga is what sent everything straight to hell. We must remember it was after the Ikaruga war that Jin lost it. Not only Ikaruga was a bloody war, it was a complete setup by Terumi, Jin not only stained his hands and caused suffering, the reason he believed in to do so; a greater good was non existent, Jin realized all he did was a simple slaughter.

I see legions of soldiers
... who've lost all sense of purpose
... While relentless danger pins them down

He has almost lost his will, he sees others without a true goal, just living until pain consumes then and he is one more now.

I must take a stand if
... there is to be another day
I must give them hope to believe

A faint idea and hope stands in him, that he must guide them, show them a porpuse a belief, since he realized the emptyness of life he must seek a dream or objective to move on and save others that have fallen like him. Everything that's passed
... and all before me now
... leads to what I've become...

Pretty much his ideas and convictions are made from the pain of every experience, he wants to do something to help people so they won't have to experience what he had: the guilt of his own mistakes and the lose of a porpuse.

For I... I must choose the path before me
As protector, sworn and true,
Steadfastly watching o'er the world,
Fate has death me the jokers and kings,
A hand I cannot refuse.
Ready to fight.
Forever... Alone

Same as the last time.

Who I am has become a mystery...
But what I do will live on as legendary.

He doesn't know what has happened to him, where his resolve went, why he had hopes in the first place. His will has shattered, his ideals vanished, he no longer cares about anything, he doesn't understand anything, he can't fight anymore. Even he himself can't understand what has become of him without porpuse, yet he is claimed as hero by people, but nobody understands that his achievements are empty, he is no hero, just a tool, a weak man that only hurt others in his life and still nobody can see the truth.

Join with me today,
We can make a difference to the world,
... to People in the streets everywhere

This is Yukianesa talking, this is Saya's legacy. The sword, she can give Jin power, the strength to do justice, a light of hope for Jin who has foresaken everything after Ikaruga.

When we fight as one
there exists no foe we can't defeat.
Come take up the cause and fight

More convincing words from Yukianesa, she is luring Jin or better said; she is inviting him to a test, a mission that if he can accomplish he will become strong enough to change the world no matter the odds or the opponent.

Fight beside Jin Kisaragi...
The protector, sworn and true,
Steadfastly watching o'er the world.
Strong within the hand of fate
Our Honor WILL prevail
Destined to fight...
Forever as one....
This time Yukianesa says this, she will be Jin's weapon, Jin a hero for the world, who can watch over its people, with the power to whistand anything. Both will go on, they have a mission and a hope to restore balance and order to make a better place, but they must do it together.

In conclusion:

Yukianesa is not an evil entity per se and Saya didn't give it to Jin to mess up his life. Yukianesa is a test that Jin must surpass, an incredebly hard task, but would Jin succeed and he will gain power beyond anything. The sword makes Jin unstable by amplifying his emotions, reason why Jin's chaotic mind is like that, pain suffering, guilt and inferiority are all increased to extreme levels. For that reason Jin's power of Order is weak, Order and chaos are opposites, one cannot exist where the other resides despite they need each other, and since Jin power is Order his mind corrupted by his fate simply blocks his own power. Yukianesa is, however, needed, it holds the key to Jin's power, the true strength that can change the world. Jin is the antibody to destruction, a hero, he wants to save others not to feel himself better but to actually do something to help people. However the task of controlling Yukianesa and his own experience has grown too much for him to handle and so he has foresaken his ideals and given himself to his obsessions.

However Jin is overcoming this, he is growing into the hero Saya hoped. Yukianesa is not meant to restrict Jin, it is meant to lead Jin to his true power, but only if Jin has found his path and ideals in a road that is easily to get derailed from, when that happens Jin's mind collapses and his power is blocked, that is why when Ikaruga war was over Jin changed; Yukianesa's test was still going but Jin couldn't handle it and his emotions went astray, his Power of Order and love for his brother made a mix that leads to his twisted reactions towards Ragna, should he love his brother or despise and destroy the Black Beast, theat to the world? And also what made him despise Noel too, he didn't know but more than seeing Saya he could feel she was also a threat to the world, and in the end it was right, Noel is Kusanagi so his hatred for her was at full, but he no longer cared to do something about it or try to live on with it like when they were at the academy.

This is also the reason why Jin can't simply get rid of Yukianesa and pick up another sword. He has to get over this in order to be the true hero he always aspired to be for the world and only with a strong mind he will accomplish it.

Something that also depends on Jin's mental state is how strong he is: while chasing Ragna he is weaker than Noel and Tsubaki (who even herself is shocked she could defeat Jin), I doubt any of those two could take a whole army by themselves (Mu aside), while Jin did so in Ikaruga and only in 2 days. It was a setup, sure, but Terumi stated several times that his power of Order was what made him the perfect candidate to strike Ikaruga, the power was convenient for him to easily take down the country and take whatever he needed from there, and I seriously doubt a whole nation of ninjas is made entirely of chumps. When he lost it after the war his power was cut since discord invaded his mind and hence order weakened. Ragna said Yukianesa was using him, but by that moment Jin's obsession with Ragna was stronger than ever, when that happened Yukianesa gave up on Jin and refused to work with him anymore, reason why Jin couldn't even unsheath the sword. However, when he could get his head straight when facing Tsubaki and his mind was made up for once in a long time he not only regained the trust of Saya's legacy, his power increased dramatically, he could fend off Tsubaki who had beaten him earlier, he could pinpoint Phantom in mid battle, destroy the field, track down Terumi and kick his ass forcing him to flee, with Yuuki Terumi even admitting that if they had continued he would have lost. For Hazama to admit that so right away, not be shocked, not use his BlazBlue and just run it must be a pretty solid fact that Jin holds immense power.

This is also why Mu acknowledged him as a threat as big as Hakumen. Despite that Hakumen being at just 30&-40% of his power, he was strong enough to corner Ragna easily at 20% of his own power in CT until Ragna used the BlazBlue, in that game Ragna without his trinket could easily destroy Jin.

This however remains incomplete, reason why Jubei has taken him with him and why Rachel as well has placed some faith in him, regardless that aside Tsubaki, Jin never had a friend or nobody, and with Tsubaki gone mad he is pretty much on his own, but since he is capable of changing the world for best others have begun to count on him. At first he didn't want to do anything because his ideas were all destroyed by his experiences and gave himself to his obsessions, but now has someone to save and has finally returned to believe and aim to do what he believes it's right.

So here is what I think in terms of power:

Perfect Order Jin (if he and Yukianesa can synchronize as Saya hopes, full power of Order)
Sane Jin (Pre Ikaruga and post fight with Tsubaki, partial power of Order)
Psycho Jin (After Ikaruga, with his mind astray, minimun power of Order)

Perfect Order Jin = Ragna's True Power (wheter has the Idea Engine or he is as bestially strong as he showed to be in Phase 0 to hold his ground for a year against the Black Beast, Jin is mean to become his equal) > Sane Jin > Terumi (BlazBlue Active) > BlazBlue Ragna > Terumi> Noel > Tsubaki > Psycho Jin

Also we have to remember that is not power to fight alone what the Power of Order gives, it also gives the power to deflect and destroy phenomena intervention, the same actions that have messed up the world. In other words, would his power of Order be fully active Jin would be practically immune to fate itself, that is why he can bring order to the world, he will not be manipulated and can bring his harmony to the planet.

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