With the app you get High Quality (not HD) on Wifi and Low Quality on 3G. That's it.
With the mobile site, use the "HQ" button under the video. It should be red before you hit play on the video. It's not the full HD version, but whatever version it is it's a version that looks great on the iPhone 4 which is all I care about.
Try this on your iPhone with the HQ button turned on: