Nintendo: Personally I dont think the Wii is very good. Its way too overrated. The best part about it is probably the cheesey but slightly entertaining Wii Sports.
Microsoft: I love the 360. To me its the best console out there right now! It has a few good sports games but mainly shooters which is great.
Summary: Clearly I pick Microsoft and the 360 because I think that they have better graphics and has way better games.
Nintendo has the Wii which almost only has games for little kids. Its lame and again way overrated!
microsoft. its meant for more adult players even though they made it more kid friendly. and nintendo is meant for the family not single guy taking on 5 more people on xbox live. also the online on the xbox is the best out of sonys and nintendos...just to make that clear too.
Nintendo owns Microsoft. not many people know, but during the construction of the PlayStation (or even before that) bill gates somehow got the idea since the PlayStation would soon sell a lot, he thought that if he somehow made a console, he would make even more money. And the ironic twist is 25 years before that happened, Steve Jobbs of Apple Computers released the Apple 1, and Bill Gates stole some memory from the Apple 1 to make his PC (I'm using a PC anyways)
Bottom line, Bill Gates is a Billionaire because he copied other people's ideas
In this case I'm unbiased. I have a wii and an xbox 360, and I love them both. Right now Microsoft has way better games out there, a more expensive but awesome online gaming base, and a media player in a console practically. The wii's online is fun but friends codes are just a pain. There game out right now are way more favored to the casual gamers, and the hardcore gamers get nothing. Wii can give some great and awesome hardcore games ,but as of now I prefer my xbox.
I'm a much bigger supporter of Nintendo than I ever have been, and ever will be, for Microsoft, but as a more mature gamer, the 360 has a lot more to offer than the Wii.
I have both, and I love both, but the only games to come out for the Wii that blew me away were the giants: Twilight Princess, Super Mario Galaxy, and Brawl. No More Heroes was cool, but it only seemed like half of a game. The Wii hasn't helped spark any new franchises whatsoever, to my knowledge at least.
The 360, however, has a never-ending supply of hotness flowing from it. Assassin's creed, Fallout, Left4Dead, Halo, Gears of War, Shadowrun, Fable, 3N, etc. It has started and continued, successfully, multiple franchises that will be with us for a long time.
For a quick good time, the Wii is the better option, but for a serious gamer, the 360 is a fairly clear choice. As far as handhelds, Nintendo will never really have any competition. The Ngage and the PSP tried, but both of them suck compared to the DS Lite. Thousands of games across the gambit of genres makes it so that the hardened gamer and the housewife can still find something fun to play.
As far as history goes, I'll have to side with Nintendo, but as far as the better core system for a true connoisseur of gaming, Microsoft has that one in the bag.