The biggest trade-off to the new origin is removing Victor's sanity before the freezing incident and eliminating the actual love between Mr. And Mrs. Fries. This is not significant change to the manner in which Mr. Freeze is written (which is a wonderful thing) but it does change the way Victor's actions are perceived and read. Without his wife, he becomes a somewhat cliche horror villain archetype, twisted by a madness that most of us will never experience and may find hard to relate to, since his connection to reality is utterly destroyed in favor of a delusion. He mainatains the same fear and horror he should instill, but he's no different than someone like the Mad Hatter or Maxie Zeus in that he's vageuly sympathetic but ultimately most of the audience feels confident we would never act like that. And his transformation isn't as tragic as it could be; it's more like karma making an already dangerously deranged man into a reflection of his inner issues. We don't feel as sorry for him as we once did.
With his wife, he becomes a Byronic Anti-hero, extremely emphatic and easy to understand on a visceral emotional level. We all have a strong idea about what it would be like to start losing a loved one and can understand the desperation and despair of trying to stave off death for just a little longer. But Victor might actually have a chance of doing so, so most of us would probably agree with his willingness to break a few laws to preserve a true reciprocal love bond with his wife and to try and save her. Heck, his actions can even come off as radically valuable medical experiments with quite logical and practical science behind them. And then when he is betrayed (over the monetary cost of his wife's life to a faceless corporation) and horribly cursed with his new life, we get pissed off right along with him. His new world and all it's strak horror is a cruel injustice, making his horrific MO and brutality horrifying because a lot of us would be extremely tempted to do the exact same thing in his shoes.
"Think of it, Batman. To never again walk on a summer's day with the hot wind in your face and a warm hand to hold. Oh yes, I'd kill for that!" "I failed you. I wish there were another way for me to say it. I cannot. I can only beg your forgiveness, and pray you hear me somehow, someplace... someplace where a warm hand waits for mine."
Both phrases could be uttered by a Freeze with both his old and new origin, which is awesome. But if the latter says them, we just think of a crazy man talking to himself in unrealities, while the former is a grim statement we wholeheartedly agree with even as he does horrifying things.
And Arkham City has a seemingly perfect formula for Freeze as a sustainable character who belongs in Arkham in a continuing series; Nora's his wife, she's still frozen, and he is still desperately trying to create a cure for her disease even while she looks like a dead block of ice. His search for a cure and his obsession with that provides plenty of excuses for why Freeze will continue antagonistic attacks on his opponents, why he might do mercenary work, and why he's still pissed off. She is for all intents and purposes dead, but there's still a slim small hope that she could live, so Freeze will not brook any delays to her recovery or threats to her person, and it's possible her even worse condition than tradionally depicted (floating in water versus actual block of ice) is just another sign of his boss's betrayal.
And arguably, this Freeze is far more effective of a character and supervillain than any other adaptation to date: he's still sympathetic, but more sociopathic and deadly, and he's almost certainly still gunning for Batman if the context changes and he thinks Nora's endangered again. It's effective, keeps the old origin, and can be just as mode locked as his New 52 one. Akahm's current depiction is better, and much more applauded, than any comic version in the last two decades. They killed her off Post-Crisis, and he became a less interesting thug. They removed their marriage New 52, and he remains largely a less interesting thug. But if his wife's still married to him and still ever so slightly resuscitatable, he's someone we can root for and against at the same time, and that's much better than Maxie Zeus with an ice gun.