There isn't much outside of content, it's mostly little things. The biggest difference is that the SNES version has a vs. computer mode that the NES version lacks, probably because it couldn't handle the A.I. script. The Round Game is endless in SNES, but it tops out at 99 in NES. In NES, the Round Game has a "Type B" mode which has a boss at every tenth stage. The music has different compositions for each game. The diamond item can be moved in SNES, but not in NES. That's all I remember, there might be one or two other things.
Yoshi was released on NES and Game Boy, and Yoshi's Cookie was released on NES, SNES, and Game Boy. With those, I believe there was no difference besides graphics and sound.
Dr. Mario was never released stand-alone on SNES, it was released in the dual-pack Tetris and Dr. Mario.