No, it does not play the 1080p version when I'm on Wifi.Whatever resolution while on a 3G network is lesser. If you're WiFi connected it will give you the best resolution possible. There is no standard resolution though simply because they differentiate between videos. One think you can do to play higher quality videos on 3G would be to go to Youtube.com on Safari and select [HQ] on the video page.
*CDMA USERS*It's 240P for GPRS/EDGE. 360P for UMTS/HSPA/HSPDA and 'HD' on any WiFi network regardless of the WiFi being slower then a cellular connection or not.