The N64 and the GameCube both are my favourites, but if I had to chose one, it would be the GameCube. I just loved the immense jump when it comes to graphics - and when I look at them now, I still think they're very breathtaking. Everything looks shiny and detailed, I love it so much!
Also, a lot of my favourite games are on that console. Mario Kart Double Dash, Kirby Air Ride, Super Mario Sunshine, Melee, Windwaker, the two Pikmin games and many more. The library of the GC also was just massive in my eyes, and all the games were of really high quality and have a high replay value.
When it comes to the N64, I still love the games, but yeah... A lot of them feel really awkward. Especially Mario Kart and the original Smash Bros are really weird to control. But else, I really enjoy Super Mario 64 (well, who doesn't), Kirby 64, the two Zelda games and a few others. But well, most of those games already got remakes and besides Majoras Mask and Super Mario 64 I tend to only play the remakes.