Just to add to Ferny's thing about genres, it's not like fighting games have been well representing either, most aren't doing too well and the two best-selling for the entire generation are Dead of Alive 4 and Super Smash Bros., and since Team Ninja is basically dead now, that really only leaves one relevant fighting game left.
And yet despite all this, it is true that the Wii does have more genre variety. It just has more titles in more genres, either the best in the field or solid entries in their deficits. There are whole genres that the 360 and especially the PS3 ignore or relegate to "download game" (say it with a sneer). And as the userbase grows it'll get more, where the other two will refine their games and probably only represent a few genres by the end of it, sorta of like the N64, except without Nintendo's last minute attempts (like Paper Mario and Animal Forest (in Japan))
IT isn't as stark as DS vs. PSP, where the DS has a game for every genre and possibly every profession (doctor to stock trader to bartender), and they are the best in every field, sometimes by default. While the PSP has it pretty much narrowed down to PS2-port-nobody-bought-the-first-time. spinoff-nobody-really-wants, or original-game-nobody-buys. It's why the PSP's 2nd redesign probably won't do much. The DS Lite hit at just the right time with New Super Mario Bros, having a piece of software drive the hardware. The PSP 3000 just doesn't have a game anybody wants with it, so Sony's resorted to Nintendo-GameCube-style bundling.
But I digressed. The Wii has the most genres filled and will definitely get more as time goes by and smaller third parties fill the gaps the bigger ones don't want to. Even RPGs, which the 360 "leads" now, if only because they are willing to shell out more than they are really worth, only to have them flop in Japan and kinda do the same here, and like Ferny said. Since 2005, there's really only been a handful. But a crapload of them for the Wii were announced during TGS and you know there will be more, especially as the userbase grows. It's just what being the market leader entails.