The HD6770 & HD6870 are in difference levels in the performance brackets. In fact the HD6770 is two levels lower than the HD6870. 6770 is not economically recommended for crossfiring at all.
The main question is what do you want the crossfire for? If you only play on 1920x1080 monitor, a single 6870 is enough for great performance. If you want to play on triple monitor, then yes, you need at least CFX 6870.
the hd 6770 is rebadged of hd 5770 there is about 1-2% difference between them which means nothing the hd 6870 is way better then hd 6770 the hd 6770 comes in low - med level gpus and hd 6870 comes in med high level gpus so there is no way to compare the hd 6770 to a hd 6870 the hd 6870 is way faster an better.
The 6870 will give close to double the frame per seconds ( determines how smooth your gaming will be ) compared to the 6770 at less than double the cost. Therefore, it is the better buy.
Yes. Your motherboard can accommodate 2x6870. But the more important question is what is your power supply? The 2x6870 will require 4x6PIN PCIe connectors and recommended 600W capacity.
Why you want 2x6870 is still an open question. If you tell us the reason, we can give you even better option than these.
& what is you monitor resolution? Ex: 1920x1080?
My power supply is Xigmatek Go Green Bronze 800W Modular Power Supply
My screen resolution is 1920x1080
My casing is CM Elite 430
My MoBo is GIGABYTE GA-Z68A-D3-B3 SOCKET 1155 MOTHERBOARD
can power supply xigmatek in my casing?