I have the very similar Sony V3. One thing I have noticed is that the Zeiss lens on this compact can outresolve its pixels. Of course there is noise but at 100ASA it rarely shows up. If I make 18x12 prints (from processed RAW files) it is impossible to tell they are from a compact. In fact, they are crisper than prints from any 8-10Mp DSLR with kit lens that I have tried and equal to something like a 30D with a 24-70L attached. As I write, I have a lightly cropped 18x12 V3 print of a fern leaf in front of me. Beside it is a similar, uncropped print taken with an Olympus E300 with the 14-54 lens (a reasonable zoom). Everyone thinks the Sony print came from a more expensive, fancier camera.
I see no reason why a Canon G6/7 can't achieve this and if it doesn't, it could well be faulty. I would suggest you do some careful tests using a tripod and detailed test subjects, shooting in RAW. If the difference is still as great as you say, maybe you should get the G7 checked out?
Don.