The 7970 is a bit better than your 5870s dependent on the game and you would not have to worry about the game supporting crossfire.
It is true, you won't have to worry about CrossFireX issues and newer games would probably run more consistently with a single HD 7970. You have to take a step back and look at the money you are spending on one thing if you really don't need it. 550 dollars or more is quite a bit to spend on a single graphics card especially if you already have two very capable cards. It would be a different story if you were building from scratch or had a pair of lesser cards.
You may see a nice bump in performance in BF3 but Skyrim is also very CPU dependent. I often see many lows as well, especially in the cities where the CPU becomes more important than the graphics card.