This is the first mention i've seen of screen tearing being a problem with multi-monitor gaming. Have you checked widescreengamingforum.com for solutions suggestions to resolve the issue or a confirmation that this is an AMD specific issue? Easiest solution is to fix the issue and keep your card.
If that is not an option then you are going to want the horsepower of the 570,... downfall is that the 1.28gbs of VRAM will be a limiting factor at 3x1920x1080 if you go multimontior at a later time with another 570.
THe reccomendation above for the 560ti with 2gb VRAM for each GPU is what you would want, but i'd look into triple monitor performance with 2 of those cards. I dont think it would perform on a desired level for multimonitor gaming.
Edit:
http://hardforum.com/showthread.php?t=1576329 has some good information on screen tearing and Eyefinity setups.