We both technically have access to, card for card, exactly the same number of things. One trial deck, one booster box, and five loose packs. So it's not that he has all the Persona sets to pull from at this point, just that he seems to have a lot of powerful events that I can't match.
The deck I was using only has one event in it, the blue Juneketsu (level one, zero cost, look at the top for cards and put a character in hand and the rest into the graveyard) and the one time I used it I fucked myself by getting a level zero and discarding three climaxes. Compared to "search your deck for anything" and "bury any of your opponent's characters in the stock so they'll never be seen again" there seems to be a power level disparity.
To be fair my characters were mostly able to overpower his, but after a point he just didn't care about combat any more because he could kill all of the characters I went way out of my way to get markers on instantly with no chance for me to fight back. I had card and stock advantage for the entire game because I was running combat, but his endgame card quality was way too much for me to handle.
I think my climaxes were kind of goofy though, I didn't really have anything that boosted my whole team's soul so I never had the chance to take advantage of my early domination of the board by just clobbering him for like fifteen damage in one turn. Of course doing that is just begging for my entire turn to be cancelled out by his climaxes, so yeah... Not really sure what I'm supposed to do. But having a problem to solve is fine, I'll figure it out.
I did learn that the level one Inumuta who gives characters in front of him +500 power and +1 level ("Inumuta, Genius Hacker") is amazing though. Since the Kill La Kill characters tend to be so overwhelming in combat people seem to just stop fighting me and go for all side attacks toward the end of the game, which means all my backups are wasted. Inumuta makes my guys much harder to get around, so my opponent has to fight my characters to get at me, and then I can just crush them in combat. And he even draws cards. Seems like a definite three-of, and I've only got one right now.