As a former 35mm slide shooter eons ago, I knew I'd eventually move to full frame from my 'starter' 30D. I upgraded to a 60D for more megapixels as I sometimes do rather tight cropping...ie, changed my mind from when I took the shot. Low light with the 60D at church functions (usually without flash) was a challenge, even with my 16-35 f2.8L ii and the 24-105. I tried a 24-70 L a year ago, but just too darned heavy for these old hands and no IS, so it was sold. While I found wide-open with the 135 L gave me enough light for reasonably fast exposures, but with the 24-105 I use mostly, it was either slow exposures or moving to the "uncomfortable ISO" speeds over 1600. I opted for slow exposures and dumped a lot of pix with subject movement as a result. As far as 24-105 distortion, Lightroom corrects it with a single click.
So, "feeding the need" for better ISO, I went to the 5D3 just before Christmas. What a difference! ISO 5000 and up is no problem! For me, the 5D3 is the ultimate solution to low light! Handheld shutter speeds 1/125 and faster are a joy. And even at f8 or smaller for DOF, the results are still outstanding! But when I want the ultimate low light, thin DOF, the 135 L wide open wins hands down!
So, based on my 60D experience with the same sensor as the 7D (and perhaps better firmware?), if the OP has the money, go for the 5D3. The 6D ain't no slouch, either!