What features are missing in the Wii edition of Rock Band 3 that the other (PS3 or Xbox 360) editions have?
Gameplay functionality only, not console characteristics such as video output resolution.
I have a few to add that might count as console characteristics, but they impact Rock Band (especially DLC downloading) so heavily that I think they're good to know. I originally wrote these up ages ago before Rock Band 3 came out, soon after I migrated from Wii to Xbox for Rock Band 2. These are features of the Xbox experience that make it (IMO) less frustrating than Wii on a daily basis:
The RB instruments are for-real first class controllers. Every day sitting down at the wii I had to dig out a wiimote to press A, choose RB, press Start, and pass the stupid "don't hurt yourself with the wiimote" screen. Then I put it down and never touched it again and drove from the drums. On the box I can power up the console by turning on the drums and never touch the controller that came with the console. It's really convenient by comparison.
Downloads are done as background processes. I can't be the only one who gets driven mad by having to babysit DLC downloads on the wii. "I'm done downloading!" A. "I'm done moving to the SD card!" A. "I'm done refreshing the DL list!" A. "Look at me! Another pointless message for you!" A! A!A!A!AAAAAAAAAAA! Leave me alone and do your damn job you stupid machine! On the box not only do you NOT have to respond to pointless messages (definition of pointless: the only choice is to press A), you can start a download and go back to playing or tweaking your avatar or whatever.
xbox.com integration. This is on a thin line between awesomely-convenient and deadly-to-your-wallet. Related to how downloads work above, you can go shopping on xbox.com from your web browser and the next time you fire up the console anything you bought will quietly start downloading and give you a little notification (which does NOT require you to press A to dismiss) when it's done.
Online friend notifications. Another task I won't miss is making repeated trips back to the Invite Friends screen to see if any new players have turned up. xbox pops up a notification (kind of like the one you get from RB when you get an invite) when anyone on your friends list comes online.
Disclaimer: I think RB3 might have fixed the 4th point (I don't own it on wii so I'm not sure), but I'm pretty sure the other 3 still stand. If RB3 fixed some of the others I'm sure commenters will let us know...