Anti aliasing does depends upon the memory size, but it depends upon the GPU horse power too. And regarding memory usage, don't judge all the games by the memory usage of Skyrim. Skyrim can use very high amount of memory, can easily exceeds 1GB memory usage with ease even at 1080P or lesser resolution whereas for most of the other games it is uncommon.
And Sukesh, if you enable very high AA, 4X or higher, HD 6770 will always perform better than a HD 6670 if both having same size and type of memory. It should be as enabling Anti Aliasing also increase the level of computation apart for the graphics data size. Otherwise a HD 5570 with high speed GDDR5 memory could have the same Anti aliasing performance of a HD 6770.