Yeah, its mostly due to BP that you're losing, since people that can afford Ay generally have a significant combat power advantage.
That being said, with equal BP it is possible to win. Just took down a Ay/SSK Susanoo team that had a 4k power advantage on me yesterday in matsuri with a Cho-Mei water team because I beat him in initiation. People that run Ay in p1 are pretty much giving up R2 skilling, so if they dont kill one of your ninjas in R1, R2 is the chance for you to stabilize. by interrupting the obvious mystery user/weak link in the opposing team. Got to put out that the opponent wasnt really thinking about his lineup much though, he was using light main, guy, raikage and ssk susanoo, no barrier ninja, which helped me survive R1 (though since I won him in initiation chances are my barrier would have won too)