The Wii is simply not capable of the same level of graphics that you'd expect from an Xbox 360 or PS3, so the effects, models, audience, etc. will all be toned down to different extents. Do consider, however, that most people don't play Guitar Hero primarily for the graphics. The actual gameplay is pretty much identical.
Earlier versions of the Wii Guitar Hero and Rock Band games had issues with the lack of DLC (Downloadable Content) which made the Xbox 360 and PS3 versions far more desirable. I believe that this has mostly been rectified now.
Also note that the Wii suffers greatly from the lack of a real multiplayer (online, not offline) implementation. You will find far less people playing any game online with the Wii than you would on its Xbox 360 or PS3 counterpart. The other consoles make it more seamless and integrated to communicate and play online.
Ultimately the Wii offers an inferior experience. Whether or not this will impact your enjoyment is reliant on how you plan to play the game. I own Guitar Hero 3 on the Wii -- also my only console at the moment -- and have enjoyed countless hours of fun with friends.
If you foresee yourself purchasing another console any time in the future, I'd just wait until then. You're probably going to be spending a lot of money on instruments, so I would say it's best to have them compatible with your favourite console for future versions of the games. If you're sticking exclusively to Wii, however, and like the franchise, then go for it.
On a related note, if you haven't yet tried the Rock Band series and like Guitar Hero, it's definitely worth doing so before you purchase Guitar Hero. They're very similar games, and the instruments are mostly cross-compatible, but Rock Band 3 has some noteworthy additions that aren't to be found in the current iterations of Guitar Hero.