Since i am a fan of both microsoft and nintendo I am afraid I am gonna have to disagree with you.
Nintendo have always been known for creating adventure games (examples: Mario, Zelda, Banjo, donkey kong, final fantasy etc.)
However microsoft (X-Box and X-Box 360) Are known for designing FPS and Racing games (My favourite Platforms) (hey, more use of brackets

)
Anyways people who dislike famous X-Box games such as Halo, PDZ (omfg perfect dark was for nintendo as well) and Quake tend to dislike the console as well.
Basically you cant say one is better than the other, its all down the the type of game you like.
If you are a big fan of Adventure/RPG games but dont like FPS and such will like nintendo more. However if you like FPS more than adventure then you are more likely to be an X-Box person.
I myself like both genres so I like both consoles and both companies.