I have the 7D (which is very similar in IQ to the 60D) and the 6D. If you shoot in good light and don't crop heavily, the only differences will be those caused by the crop factor (or lack thereof) that cls mentions above. If you shoot in low light, the 6D wins hands down. It handles high ISO (3200 and above) much better than the 7D. But as also mentioned above, the really big difference in IQ starts behind the camera. Learn your craft first. It took me a long time to even begin to consider things like how the light was really affecting my images and how shutter speed was so crucial to sharp images and how shooting wide open all the time wasn't allowing me to get the best image. I still struggle to remember to check my background for distractions and to try to make sure my camera is level. I still look at images from the folks on this board and think how much I still have to learn.

Another thing you may consider is your glass. If I separate out my best shots, they're almost always taken with my higher end glass. The exception there being some of my favorite shots that came from my Roki 8mm FE, which is a dirt cheap lens. All things being equal, a good lens on a 60D will trump a so-so lens on a 6D.