As a Bulls fan for decades, I've followed Rose like a hawk from the outset. Last year was mixed feelings. He paced himself to play the entire season without a major injury, but that meant dragging himself up and down the court in the first half of the season, while still pacing himself in the second half. He turned it up around January, but mostly only on offense, unless it was a nationally televised game, which he gave it everything (and was usually awesome.)
So I think the change of scenery, and to a huge market, will bring out the best of him on both sides of the court. Playing with stars in front of that audience will inspire him to fill the box score, and not just in the scoring column this time. He's only 27 and has a lot of game left in him. He's one of the few guards that can keep up on defense with Irving, Wall, Curry, and Lowrie (although tended to get toasted on pick and rolls by guards that go straight to the cup, like Teague and Lin.) At the same time, he can get whatever he wants off them offensively...if he's willing to play that hard and his conditioning is back up to top form, which it wasn't last year (with only himself to blame.)
In NY, if he's on the court and fairly uninjured, he'll take these matchups personally again and do very well, better than he would if still in Chicago, where last year he was thinking he's great but wasn't concerned with being great every night. I think he put Chicago in a very difficult situation, with many fans having turned against him (albeit often ones that listen to more talk radio jibberish than actually watch him play much imo.) As a result, management really had little choice than to trade him, when they knew they were never going to offer him what he would want after a good year (because of the health risks, age, as well as questionable desire), and could get nothing for him if they did nothing.