I'm not actually a student at any of these (have accepted another uni) but I did apply to and visit UEA. I really liked the campus, the park it was situated in was beautiful, the sport facilities looked really good, and I even liked the architecture (even though I'm a stickler for old buildings). It's a bit of a concrete jungle, but the Ziggurats (pyramid like buildings) are strangely beautiful, and as a whole it felt welcoming and was easy to navigate. Also, Norwich is a lovely place, if you like pubs, old buildings and markets (which, incidentally, I do). Friends who go there have said the club scene in Norwich is a bit quiet, but this is made up for by the events on campus. In the end, it was just a bit too far from home for me.
I don't know much about the other two, other than that Liverpool is another lovely, if very different, city. The overall league tables (TCUG and Guardian) rank UEA above Sheffield and Liverpool, but this may be different for whichever subject you're doing. And league tables provide limited information really, if you're genuinely torn between these places based on your initial impressions, you need to go and visit them in order to truly assess their merits (assuming you haven't already visited), in relation to what you want from a uni.
Good luck!