Re: All Graphics Cards related queries here.
^^ Yes true, the 5xxx series give your DX11 and tessellation. But not many games have that as of now. Even with DX10 games looks nice.
I never mentioned that the image quality will be the same on both cards -- provided you are running a game written for the DX11 codepath. There are not that many games available currently for DX11. By the time DX11 become mainstream -- the 5xxx will be old.
Sure, go ahead with the HD5750, but do remember it does not have 'that' much processing power. For the same amount you get a board with more guns (Hd4870).
Regarding your query:
I would personally give priority in the following manner:
1. ROPs, TMU, TUs. (they are the basic processing units, more the merrier)
2. Engine Clock. (how fast the processing is going to happen. How many cycles per second)
3. Memory Bandwith (this composes of Mem. Type and Mem. Clock -- how much data can be loaded and quickly available to the engine). This is what feeds the engine.
Transistor count is the overall broad picture. The more transistors on the core -- the more of (1) you will have.