See below review link which has direct comparison benchmarks between the HD 4770 and the 1GB version HD 5770. Generally speaking, the extra 512MB will only add about 2FPS when playing at less than 1920 x 1200 from previous benchmarks I've seen. Also, in more rarer instances, the extra VRAM can sometime reduce performance by 1FPS or 2FPS.http://www.xbitlabs.com/articles/video/display/radeon-hd5770-hd5750.html
The HD 5700 1GB is faster than the HD 4770 by a decent margin, but in a few case it seems to only perform as well as the HD 4770. Keep in mind that drivers are still immature for the HD 5xxx series so technically speaking, there is still room for some improvements.