Both are great, but you will probably play Puzzle League more.
Then it came out on N64 as a Pokemon game. You had to win your way through all the gym leaders, and then Gary, and, if you were good, you got 1 chance to beat Mewtwo.
This time, you choose the graphics, logos, music, and the rules as well. Making it much more than anyone expexcted. Pay a visit to the options menu when you buy it, because the default isn't very good.
Dr. Mario is similar in a way, yet there is less to customize as you play the old game in basically the same way. The only difference is that they have a new music called "Sneeze."
Puzzle League has definitely advanced, Dr. Mario not as much, but that doesn't stop it from being fun.