Dedthread? RIP. It hasn't been a month since the last edit, so I'll just necro this I guess. Otherselves don't seem to have conventional stamina, nor does grievous injury bring them closer to death. Both IBRS and BGS were shown to be just as active when down a limb; they just had less appendages to work with. Considering that, I don't see Vegeta winning by incapacitation like Gargoyle suggested. The determining factor then would be if Vegeta can land an attack comparable in power to the Rainbow Cannon and destroy IBRS completely, and if he can do so before being killed himself.
If IBRS's treatment of pretty much every other attack thrown her way in the anime is indication, then she would just stare Vegeta's biggest attacks down instead of dodging, so that wouldn't be an issue. The only question is if Vegeta has the raw power to kill her. This is... hard to work out. Base BRS could survive the attacks of other Otherselves, giving her Large Star durability. IBRS's durability is higher, but exactly how much higher is unclear. The Rainbow Cannon, which used the combined powers of several Large Star AP characters, was the only thing shown to hurt her; but it also literally disolved her, so clearly there's some overkill involved. That puts IBRS's durability in the vague Large Star + range. Coincidentally, Vegeta's strongest attack at this point is also somewhere in the vague Large Star + range. Now, normally this would mean that Vegeta is in the clear, since even if an opponent is barely able to survive an attack like that, they'd usually be incapacitated as a result. But like I said earlier, incapacitation doesn't really work against Otherselves. If IBRS doesn't die outright, then she'll get right back up with whatever partially-dissolved bodyparts she has left, and keep fighting. Vegeta wouldn't be so lucky. If the Big Bang Attack fails, IBRS will be able to butcher him easily. So the two possible outcomes are as simple as, Big Bang Attack is strong enough to kill her, and Vegeta wins, or it isn't, and IBRS wins. I'll call it 50/50.
That said, IBRS wins pretty decisively when Big Bang Attack isn't involved. Vegeta's low-end attacks would all be healed from, and they wouldn't even whittle IBRS down any because of her huge stamina advantage. IBRS, on the other hand, has been shown to blow limbs clean off of other 4Cs like it's nothing. For this reason I vote IBRS.
