Looking at the specifications for these two cameras, it is easy to see that they are both looking for the same customer.
Here are two reviews:
http://www.steves-digicams.com/2004_reviews/c60.html
http://www.steves-digicams.com/2004_reviews/dimage_g600.html
And a review of the G600 from an owner in Sweden:
http://www.microsaft.com/g600/
I looked at the picture quality in the samples in the Steves-digicams reviews. They appear to be identical.
I would call this one a toss-up.
Pick the one that has the features you want the most.
...
..
.
We are about to buy a new digital camera and were wondering what the thoughts were on these two. We are not professional photographers, and although we've always had a lot of features on our cameras (this will be our first digital one), after awhile, we find that the automatic features serve us pretty well. We're primarily taking pictures of our family, but don't want to sacrifice significantly the resolution of our film camera when we're moving to the ease of the digital camera.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic