The two formats that are traditionally played in tournament are:
1v1 Swap
2v2 Versus (one Puyo player + one Tetris player per team)
Mixed 1v1 Versus (where players are free to pick whichever game they prefer) is sometimes used in less serious tournaments, but it isn't liked by some players for a few reasons: balance issues, how it arguably removes depth from puyo (tactics regarding building/blocking long chains are thrown out in exchange for a digging grind in the face of Tetris's consistent DPS), or simply that it lets players ignore learning one half of the crossover in the first place.
I personally love Fusion mode, but it's an admittedly silly mode and doesn't see wide play. In Swap mode, at least most of the tactics used in the individual games still have relevance, so it feels like you're still playing Puyo and Tetris. Fusion is entirely its own beast with its own play style, and it's almost entirely about speed and short-term improvisation due to the way that its chaining system works.
It's also completely busted and allows you to do infinite combos. Or at least it did at launch. Not sure if that was ever patched... Otherwise top-level Fusion play would actually need some kind of "mercy kill" rule to prevent matches from lasting literally forever. Like having 6 blue garbage comets hanging over your head = auto-loss or something.
