Take a look - a HD 4870-1GB compared with a HD 6770 (identical to HD 5770; same settings are used - HD 6770 run on DX11/HD 4870 run on DX10.1). Of course, i benched with an i7-920 at 3.8GHz. The OP would need a good OC on his CPU and we don't know what 4800 series GPU he has other than it is 512MB vRAM
Do you have a direct link to the latest time(before this test) you tried drivers for the HD4000 series? I guess your testing settings are different now than 1-2 years ago, but it would be a pointer regarding if AMD still tries to squeeze more performance out of them