For United States users who live in Mountain or Pacific time zones, TVE allows you to access East Coast feeds of many cable channels that air programs 3 hours earlier than the West Coast feeds that are available on Prime.
Picture quality depends on the channel. ESPN, Fox News, and FX all have picture quality that is about equivalent to the picture quality on Prime (720p 60fps at a pretty decent bitrate). In addition, TVE gets you better-than-SD resolution of channels like C-SPAN, which are typically only available in standard definition on Prime.
But for most other channels, TVE gets you a feed with a reduced frame rate, which often causes a visible stuttering effect during motion (particularly camera pans) if you are viewing content produced at 24fps (basically, almost every non-live-action TV show). Some people will be really annoyed by this, while others probably won't even notice. If you have motion smoothing enabled on your TV (I don't use it but I imagine a lot of people do), then the judder could become much less noticeable.
As mentioned by others, the only way to get Dolby Digital 5.1 is with Prime. In theory TVE channels could provide a stereo downmix that could be decoded back to surround using Dolby ProLogic or DTS Neo 6. I'm not sure how common this is in practice, though. I have Dolby ProLogic decoding enabled on my receiver for stereo sources and have not heard any TVE channels that seem to clearly be taking advantage of it.
Personally... I use both TVE and Prime. I prioritize Prime over TVE in my sources. I live in California so most of my Prime channels are delayed west coast feeds -- which means that even though the Prime is higher priority than TVE, some shows will automatically get recorded on TVE because it airs earlier. This isn't always desirable because some channels have much better picture quality on Prime than TVE. So for some of my DVR passes, I set them up to only record from the Prime channels if I'm concerned about picture quality (for example, I prefer to record BBC America shows on Prime, despite the 3 hour delay, because the picture quality is significantly better).