It probably wouldn't matter.
I haven't done any research, but there can't be a large difference.
Probably just a small one in core clock speeds. Which you can easily clock to match the other.
But it may also be different processor sizes. ie, 45nm and 65nm where the 45nm naturally would run cooler and use less power (no idea if there is this large of a difference in these two cards though).
Also check the memory interface width, for example does the 1gig have 512-bit or 320-bit or etc. Even if the 512mb card has only only 512mb in memory but 512-bit bandwidth and the 1gig have say 320-bit, it may still be faster than the 1gig card. Why? say the 512mb runs at 3600mhz gddr5 ( (3600 * 512) / 8 = 230gb/s ) and the 1gig runs also runs at 3600mhz = 144gb/s.
What's the texture fill rate? (how many textured pixels the card can handle each second).
Why not do some research and keeping the above mentioned comments in mind, and check out the toms hardware vga charts which should have a decent vga vs vga comparison overview for you.
anyway, my post sucked so I'll stop writing now. BYE!