I think hausland gave you a general overview in comparison to Logic, I’ve barely touched that so I can’t add anything to that part of it…i’ll echo what hausland said though and further it and point out that Ableton Live is called that for a reason, of course you know, it’s very much designed for live performance. I think it’s fine for constructing and completing tracks, but many people prefer to go the route mentioned of start in Ableton, mix/structure the track in another DAW. that’s not a necessity though, plenty of users mix and complete tracks and sets fully within Live. it integrates with hardware very well from my experience. rarely if ever have any issues I’ve had been because of Ableton…I use it as a hub controlling multiple hardware devices regularly.
you can always get a copy of Live Lite and try it out, or just check out some tutorials online giving you an idea of the general process and see if you like it. if you want a recommendation for a video covering something more specific let me know and i’ll see if I can find something
regarding OB, I used the first OB version with my Rytm and Live with no issues, though I basically only tested it out, then realized I didn’t really want to use it like that anyway lol, could only speculate on OB 2.0 of course…