If I recall, it's mainly character levels and gear/items. All the quests are reset, as are all the social/affinity levels. I'm not sure if the heart-to-hearts carry over, but I don't think they do.
The main draw are the 'secret' areas and the high level unique enemies (some of which are level 120+), which require max character level for the whole party plus specific combinations of high level gems to take down. In my case, I got tired of one-shotting everything I ran into, since the levels of all the other enemies stay the same (you'll be a level 80+ group fighting level 1-5 creatures in Colony 9, for example). I mainly wanted to experience the main story again, and not so much the New Game+ exclusives, hence the starting over.
As for Dolphin, it's truly the only way to play if your PC can manage it, though it takes a pretty beefy PC, even these days, to make it run well. I actually bought Xenoblade the day it came out (not knowing it would become as scarce as it did) and didn't even give it much of a chance at first because of how bad Wii games look scaled up on large HDTVs. I know better than that now, of course, but Dolphin is what got me to give the game a second chance.
