All Nintendo formats have similar banlists: All event and cover legendaries. XY allows anything else, so you can use transfered pokemon - but not ORAS megas, of course. ORAS Battle Spot has a pentagon only rule, which means you can't use pokemon that aren't born on a gen 6 cartridge. Thankfully, Between ORAS and XY you can catch all legal legendaries anyhow, although they lose event and older tutor moves. One big difference is that the Genie trio can't have defiant as an ability, since its their dream world ability and it hasn't been released in gen 6.
Battle spot is level 50, which is a big deal because of how you EV train. Also, if you run calcs you'll find differences, so take that into account when using a damage calculator. There's a guide to using evs efficiently
here. As far as what pokemon are popular, Nintendo releases stats for each type of battle, which you can find on their website
here.
I think someone on here does periodic giveaways of battlespot pokemon. I'll let someone else give you info on that since I haven't been around here too much.