Canon mostly use the 24-105 lens on new demo FF bodies as a general purpose lens, probably because of the IS, but last year when I had to decide between the 24-70 f/2.8 versus the 24-105 f/4L IS, I went with the 24-70 even though it was a bit more expensive.
Price, in fact, wasn't the clincher because where I am the f/2.8 was only 200 euros more, but what was the game changer (for me) was color and bokeh. You don't need IS if you're shooting a still subject/object just use some support (I've a manfrotto 055XPROB tripod and a 561BHDV monopod) or set the shutter speed to 1/60s or faster, or use a wall even.
I checked out literally thousands of photos on flickr (predominantly of 7D and 5D mkii shooters) using both lenses - thankfully flickr has threads for each lens as well as body type - imho the 24-70mm pics were way better.
Now I'e never used the 24-105mm IS lens, so I'm certainly no authority on it, so I listen to the opinion of others and accept that the IQ is similar between both standard zooms, and my 24-70 lens is a late copy (Nov 2011) and is extremely sharp, but the color just blows me away, both stills and video (using RGB Curves or 3-Way or Fast Color Corrector in Adobe Premiere Pro is now a waste of time, anything I add in effects is <CTRL-Z> straight away) cos' this lens does not require any color correction whatsoever.
Other features of the 24-70mm Mk I that I like are the AF speed (don't know if 24-105 is as fast) plus the really great lens hood which gives me a lot of comfort in the protection stakes (even though I have a clear Hoya HD filter on at all times as well).
Weight has never been an issue for me with this lens (on a gripped 7D feels really balanced actually) and it doesn't feel any worse than my 70-200mm f/4L IS which I guess is similar in weight to the 24-105mm. In terms of image quality, that means beautiful color representation and not just sharpness to me (although Brian's photo of the small plane cockpit is razor sharp using the 24-105mm handheld).
Finally, despite identical lens diameters of 77mm on both these lenses, the aesthetics and feel of the 24-70mm are amazing - a real brick of a lens that feels really nice in both focus and zoom rings (I cannot compare to the 24-105), really smooth and positive at the same time, which is important when you're staring down the viewfinder.