Well, the 3850 is a pretty slow processor (yet the APU concept is pretty cool).
How will you know? When you are playing a game, your processor will max out in doing work and slow down your fps, while your graphics cards is going to sit there doing close to nothing.
Some games are just more CPU bound that others. Others are more GPU bound. Starcraft 2 is pretty CPU bound, and Battlefield 3 is pretty GPU bound.
If you are looking at the 670, I would look at the 660Ti. Its only a 7% decrease in performance, and usually it comes with Borderlands 2.
I mean, if you want to go for the card, you can go for it and see how it runs. If you don't like how it runs, then you can upgrade the processor.
APU's are really good for HTPC media center builds, so you can use it for that.