Here's a comparison http://www.anandtech.com/bench/Product/540?vs=536
The HD7770 looses to the HD6870 by quite a bit in most things and only uses slightly less power so the HD7770 is actually less power efficient in a performance vs power ratio.
As far as newer tech goes, with the exception of SAPPHIRE FLEX on one particular card and PCI express 3.0 which the HD7770 cant make any use of anyway the 7770 doesn't support any newer tech that I know of.
They both have direct X 11 and similar connectivity. The 7770 may have some newer manufacturing possesses but, that in itself doesn't improve the performance in any way.
The HD6870 is just a better card by a fairly decent margin.