No you cannot Crossfire a 6850 with a 7870, and no, using a 6870 with a 6850 will not get you performance increase over a 2nd 6850. The 6870 and 6850 are compatible to Crossfire, but the 6870 will slow down and perform at the same level as the 6850.
The 68xx series cards use the Barts GPU, while the 78xx series cards use the Pitcairn GPU. To Crossfire two cards they must have the same GPU.
Personally I would prefer the single 7870 to the dual 6850's, simply because one card setups are always easier to deal with and more consistent in their performance. But it should be noted that the dual 6850's is the more powerful combo (though not by enough for me to recommend it ).