They are normally larger and actually quieter other than the soothing sound of the wake - and more usable than side balconies since wind is not normally a problem on the aft balconies. Plus you get a wider view - aft, port, and starboard. We prefer aft balcony cabins. One occasional downside is some soot may be left from when they blow the stacks to clean them out. But it has never bothered us. The cabin attendant has always cleaned it up.
on Carnival's "Destiny"- and "Conquest"-class ships, the aft-facing balconies are indeed bigger and I simply love them. Soot can be an issue, as Dave has already mantioned. However, with Carnival's funnel design, this usually isn't a problem. Noise is not an issue as far as engine or generator noise is concerned. It's just that you can of course hear the water the ship's wake.
I've whiled away many an hour sitting on aft-facing balconies (thanks Raoul, for the correct terminology) with the sound of the wake in the background as I read a book and sipped a drink. This gives me a sense of well-being that can define "relaxed".
Deck noise should not be a problem as long as you get a cabin on a floor with cabins above and below you.
Also, there have been the rare complaint (on some class of ships) where careless individuals have thrown cigarette butts, ice cream cones, uneaten pizza etc off the back of the ship that can land on the balcony.