Performance wise, the 6870's still win. Hassle-wise, the 7870 wins.
What games are you playing and at what resolution? You may not even need the power afforded by a 6870 Crossfire solution.
Battlefield 3, MW3, WoW, Saints Row 3, Skyrim, MS Flight. Mostly FPS games. I will be getting a new monitor so 1920X1080.
I would like to play all these games at max if possible.
Also when you mention the 6870's could be a hassle what do you mean? Will there be issues like driver delays?