Tbh, under standard battle assumptions, they would be 4km away, meaning Vegeta falls for kyoka way before getting close enough to use hakai aura which aizen can just dodge with equal speed
Most of the bleach's sealing can be broken out of with enough power. The only kido you should hope he doesn't argue for is jikanteishi(forbidden kido for time stop)
This one takes some time, it's not very hard to argue against time.
Also, Vegeta's hakai is wanked af on his page, there's no history erasure or whatever but that's just my opinion.
Honestly, if i were him, i would firstly argue for stats, in order to nullify Vegeta's absurd advantage that's derieved from their profiles, then i would bring mid godly>manga hakai + Aizen's op evolution and some transcendence stuff such as law manip(which is another thing his profile doesn't have) + hogyoku's fusion with aizen being done via reality warping, something vegeta has no counter to
Good luck with the debate