For GPU sieving, stick with nvidia. I have a 770 (which is really a re-branded 680) and it screams along. Make sure cooling is good as it throws off a lot of heat... I have a EVGA branded card with the ACX cooling system. In my other box I have a 570 which is no slouch, but barely 1/2 as fast as the 770. No complaints though! The "Titan" is the fastest card out there no question, but they are hideously expensive.
For Genefer, ATI is on top now. Their top-shelf cards beat equivalent nvidia due to better double precision performance, at least at a given price level. The Titan may still rule the roost, but for crunching-per-dollar, ATI wins here.
Rick is correct with his caveat regarding the "fastest GPU" page data. It can be iffy for multiple reasons. If one were to look at it over a period of several days, it would likely give a reasonable view if averaged out.