Either will do, the i3's performance over the A-10 with a graphics card in single thread isn't so much that it will make a difference with that GPU. You GPU will probably be the limiting factor, much like if you used just the A-10's GPU.
I looked up your Card it looks like it should be some better than the A-10's graphics. But all the tests were done 2 years ago on older benches than the A-10's tests. :S
I think the Apu in the A-10 might be just as good graphics wise actually.
Isn't the 6670 the card that can crossfire-x with the A-10 APU? The 6670 has comparable (/a little bit better) graphics capacity than the A-10 APU. So If the 6670 card is better than the 5670 card you would think the A-10 would be on par with the 5670 card or about as good. Not quite sure exactly.
400 steam processors (red wood) vs the A-10's 384's processors that have a more efficient architecture. I think the defining factor is the GDDR5's better memory performance. Although only 512.
Edit: changed the post around a bit
I just found a new review lol: http://hexus.net/tech/reviews/cpu/47257-amd-a10-5700/
The i3 does have a better cpu for gaming. Still sure it would make much of a difference with your card though. According to that review the difference (with a 680 lol) is about 4-14 FPS higher than a A-10 (65w). But that is with a much more powerful card than you currently have access too.