I'm a Wii owner, but I don't have a PS3 or 360 which might make my opinion bias, I'll try to be as centric as possible.
You aren't getting great graphics with the Wii, you are effectively getting PS2 like graphics on the Nintendo Wii. The Wii has focused largely on upgraded interface and game play. I haven't been a fan of Nintendo or owned any of their systems since NES, but it appears that the interface has improved. You now have channels which allow you to add to your main screen. For example, you have the weather channel, news channel (Opera Browser) and any games you purchase are also added as "channels". Unfortunately there isn't a lot of content available at the time.
The hardware is sub-par compared to the competition, except the controls. To be honest, I can't fathom playing on a PS2 or Xbox controller after experiencing the Wii. Even though the controls are problematic in many games, it is a lot more fun to use motion controls. For example, I'm a fan of the Electronic Arts franchise SSX, I owned SSX Tricky on the PS2 and had a lot of fun with it. SSX Blur on the Wii is ten times more fun to me, even though it's harder to do tricks and the controls less reliable. But I'm also keen on challenges. Currently the games available are hugely insufficient. A few titles are worth buying but the rest suck. Tiger Woods 08 is a lot of fun, SSX Blur as I already mentioned, The Bigs, Guitar Hero 3 and Mario Strikers Charged are the only ones I personally would invest in. Even these titles seem to be lacking in some game play features. The Bigs and Tiger Woods are fully furnished, but the others lack simple things you normally expect like Instant Replay or Highscores. Most of the Wii games are launch titles though, so this is to be expected. It's unclear what will be the future of the Wii at this point, many of the titles I haven't mentioned take simple game play dynamics and attach the typical Nintendo brands to them, such as Mario and Donkey Kong. Donkey Kong Barrel Blast is absolutely a horrible game in my opinion, likewise the minigame collections like Big Brain Academy, Mama's Cook crap and Wario Ware are fun for about 5 minutes then they are prime candidates for eBay.
All in all, I'm happy with my investment, it's a cheap system comparitively and I haven't encountered any huge hardware problems that PS3 and 360 owners have been ranting about. The controls are fun and my brother owns a Wii which means we can swap games and play stuff like Guitar Hero 3 together. Another disadvantage is the lack of downloadable content. Activision has announced additional downloadable content for Guitar Hero 3 on 360 and PS3 but nothing yet for Wii, presumably waiting for the release of Wii Ware next year, and Harmonics still hasn't announced any plans to bring Rock Band to Wii, which is already available for PS2/PS3 and 360. Electronic Arts is in my opinion one of the greatest game developers to date, but they typically don't make multiplatform games, which means if they prefer one system over the other, the others get screwed. My understanding is that 360 and PS3 are similarly capable in such a way that makes cross-platform design easier, but leaves the Wii out of the picture. On the other hand Wii sales are comparable to 360 sales even though 360 was released a year earlier. At some point developers might favor the rising Wii customer base.
It's hard to tell, but as a consumer for the time being I'm both happy and dissapointed due to the reasons above.
I necessarily have the passion for writing this, and you have the passion for condemning me; both of us are equally fools, equally the toys of destiny. Your nature is to do harm, mine is to love truth, and to make it public in spite of you. - Voltaire