The problem IMO is that of the 4 competitive consoles out there, 1 utilizes alternate control schemes to create a niche market for itself, 1 utilizes its long history to specialize its most effective genres and technology, and 2 try to have everything at once and come out as less effective on both ends.
The Wii may not be powerful, but it utilizes its simple operation and control premise to be more accessible to new gamers and families. It serves as a nice transitional console that's easy to grasp and thus fills its game library with kid-friendly games such as platformers, fighters, minigame collections and JRPGs. (I know there are some adult oriented games for the Wii, but just look at the Wii aisle at Gamestop and browse the ratings. Most probably sit at E or T.)
The PC is the most powerful console but less accessible, so it serves as the "final tier" of games in terms of system requirements and smoothness. Its long history has trimmed its core demographic to veteran gamers with good knowledge of computer systems, which tend to prefer FPSs, WRPGs, RTSs, and MMOs, all of which go along with the PCs great online capability. (I'm not counting emulators and controller plug-in options because they rarely run as effectively as intended and are usually only available in retrospect)
The Xbox and PS3 on the other hand have tried to hard to wedge themselves in between as the do everything consoles. Both try to be as accessible as the Wii (with their new motion control systems) but fail because of their hardware problems and reliance on online support. Both try to be as powerful as PCs but fail due to lack of effective,non-restricted multimedia usage, manufacturing costs and assembly-line production removing customization.They both try to be as good as the Wii and PC at their respective genres, but fail due to "jack of all trades, master of none"-like syndrome, where FPSs, WRPGs, MMOs and RTSs are slow and sluggish due to analog control and lack of keyboard, and platformers, fighters and JRPGs are wonky due to unintuitive controller layout and button overload.
I'm not saying the Xbox and PS3 shouldn't exist, I'm just saying they need to figure out what they do well and then specialize in those things. Nintendo didn't get to where it is by building consoles that try to do everything, they saw that they did platforming and RPGs well, so they worked at making future consoles better at those things. SEGA were good at sports games and fighters really well, but failed when trying to expand to CD based games and FMV. Very few gamers play every genre, so making a console that tries to do it all is wasted focus.
EDIT: I guess its worth talking about exclusives, but this is less "which console is best" and more "which game developers are willing to sell out to the console maker." There isn't any reason why Halo couldn't be on PC or PS3, it only is because Microsoft has Bungie's balls in a vice. I'm fine with games being exclusive to a console, but not when the only reason for exclusivity is due to backroom politics and shady dealing. Exclusive DLC? Bite my ass.