Upload & Sell: On
Here's the my current mid-range zoom line-up.
Size-wise, it's easy to see why the 28-135 is appealing -- it's the smallest and lightest of the lot. But it is easy to understand that it encompasses some compromises, including being the weakest of the four in IQ and build quality. Then again, it is the only one that is not an "L".
I previously owned the EF 24-85 and the EF 28-200 USM. The 24-85 was the weakest of all these lenses, and I kept in only about two weeks before selling it off. The 28-100 (second model -- USM version) was a decent lens along the lines 28-135 IQ, but was superseded by the 28-300L with IS. Otherwise, the 28-200 was a pretty fair lens with an impressive super-zoom range.
You can probably see why I bought the 24-105 recently. I wanted a lens smaller and lighter than the 28-300, but with IS and a broad focal range.
To answer the OP's question: Get the 24-105L IS to get the most out of your 6D. You'll be very happy with the images and range.
Here's the line-up: 24-70L IS, 24-105L, 28-135 IS, 28-300L IS.
For techies: photos taken with 1D3, 100L IS, 580II, ISO 200, f/4.