People talk shit about Sonic Shuffle, but I loved that it used cards instead of dice. Cards appear on the VMU, so each player can't see other players' cards. Adds actual strategy to huge instance of RNG that makes up most of a Mario Party game. The only thing that really bothers me about Sonic Shuffle is that you need to unlock the ability to play minigames by themselves, without playing a whole board. Otherwise, I think it's pretty good.
Frankly, I never really cared about the board portions. I just want minigames. For that, Crash Bash does a pretty good job. All minigames. Though some of the higher level challenges in the game are insane.
Ape Escape: Pumped and Primed is a great minigame collection. I like that most of the minigames are fleshed out enough that they practically control like a regular Ape Escape game, just with different goals. But the types of games are so different from Mario Party, and the entire board game aspect is missing, so idk if it actually counts.
Wily & Light's Rockboard for NES is okay. It's just the board game stuff, but it's pretty good as far as that goes.