Yoshi's Island.

Everlasting appeal, Mario 64 is a bit dated. That said, I would like a sequel to M64, or even a remaster more than another Yoshi game at this point..

Mario 64 but not by much

Damn, that's tough. I would actually say that's a tie! Mario 64 is my 2nd favorite 3D Mario game and Yoshi's Island my 2nd favorite 2D Mario game!

They're my #3 and #4 favorite games of all-time.

Both basically perfect, one's the best 3D platformer ever made, the other the best 2D platformer ever made. This would be a difficult question to answer, but since I have a definite list that put Mario 64 at #3 and Yoshi's Island at #4, I'll vote for Mario 64.

Yoshi's Island's got some solid platforming, some really challenging stages, and an epically good final boss, but Mario 64 is just way too much fun. It's got a lot of varying cool stages and fun challenging platforming. It lacks the sweet boss fight of YI, but it's a dang good one. Also, Wooly World probably covers YI well, having everything from that game minus the baby most people don't like.

Mario 64 easily. Not that I don't like Yoshi's Island but I simply love Mario 64. The level design, the way Mario plays, the variety, the incredible feeling of flying with the wing cap, Mario 64 is just pure fun!

I may be in the minority here, but this is an incredibly easy pick for me: Yoshi's Island by a large margin. 

Mario 64, while a milestone for Nintendo, never was that much fun for me and aged horribly. 

While I'll agree that they're too different to compare directly, and Super Mario 64 was the more groundbreaking and important game, I think Yoshi's Island is a more solid game and has aged better.

Without a doubt Mario 64. Yoshi's Island doesn't even exceed SMW for me, which I still don't prefer to 64.

Yoshi's Island, no doubt. This game was part of my childhood.

I only played Mario 64 years after.