Super Mario Bros 2, in the west, isn't really SMB2, it was a re-skin of Doki Doki Panic, a japanese game. Nintendo thought that the true SMB2, that after came to the west as Super Mario Bros Lost Levels, was too hard for the public outside of Japan, givinng us this different take on the series. When I first launched the game I was so hyped that you could choose between 4 characters from the Mario Universe, those been: Mario himself, Luigi, Toad and Peach.
But as soon as I started playing and going through the game, realizing that it was completely different then the first game, which I loved. I was kind of sad. You couldn't even jump on top of the enemies, and I wasn't a big fan of the verticality. That said, the game still had amazing controls, especially for its time. Just isn't in the level of the other games from this amazing franchise.