It's really easy in competitive Tetris, especially if you're matched up against someone who's at about the same skill level that you are, to feel like the game comes down to the selection of pieces you get. But, in most games of Tetris, both players get the same pieces. It really comes down to who can put them in place the fastest.
Which is kind of hard to wrap your head around, I know, so I prepared the video below where I use the same controller input for both controllers and play a short round of competitive Tetris.
It's actually pretty illuminating. Everything's the same: pieces dropped, garbage sent, all of it.
Of course there are probably variants of Tetris that don't make everything equal like this, but you probably don't want to play those.