I'll give AJ credit for winning the WWE Championship which is something that Vader never did accomplish, but honestly, what BIG names has Styles beaten? Let's see, we've got Angle, Tanahashi, and Cena. I guess you could throw in an older, over the hill Sting and other over the hill stars from his days in TNA. Angle, Tanahashi, and Cena are basically it, though. Who has Vader beaten? Inoki, Misawa, Sting, Hart, Flair, Foley, and others all relatively in their primes.
These 2 performers careers mirror each others a lot. Both have been all over and both have experienced success all over. Vader, though, was more dominant and has defeated more "stars" than Styles has. Let me whip out my crystal ball and say that maybe, in a few more years, Styles will rack up those kinds of wins and he'll become a more prominent name in the business, but after reading all the arguments and looking at both men's careers more carefully, I'd say it'd be foolish to think that Big Van Vader wouldn't come away with the win here.
Vote Vader.