The HD 5670 is not powerful enough to take advantage of 1GB of RAM regardless if it is DDR3 or DDR5. Based on benchmarks, at most a HD 5670 1GB card will give you 1 extra frame per second.
The basic differences between the HD 5770 and HD 6770 are:
1. All HD 6xxx cards are only PCI-e 2.1 card. No PCI-e 2.0 cards are produced.
2. The HD6xxx cards have HDMI 1.4a connections as opposed to 1.3c. Generally speaking it can handle 3D movies and 3D games.