Personally Go for the R9 290, it out performs the GTX 770 by quite a bit, and even competes head on with the GTX 780.
I would advise leaning towards a 290 with a good cooling solution, as sometimes they can get a bit hot.
if heat and noise is your issue and you don't care about losing a few frames get a Gigabyte gtx 770 4gb.
if you want highest performance with lowest heat and little noise grab a GTX 780.
if you want best bang for buck but don't care about some extra heat and some noise then get a R9 290.
Hope i helped out
Enjoy your new GPU whichever option you choose.
PS friend of mine has a Gigabyte 770 4gb, very solid card, he doesn't have to fiddle with settings and on top of that i never hear the card ramp up at all, so its definitely solid on the temp and noise front, and a very good contender when gaming.
BTW i run two KFA2 560ti LTD OC in SLI, they have less than 2mm of clearance between them and they have 92mm 4k rpm fans, they get really loud, so i know what im talking about when it comes to GPU noise and temperatures