My 5d3 is really great. I'd really recommend moving to the 24-70 (v1 or v2), or what I've finally gone for is some primes. I'm currently using the 40mm f/2.8 pancake (handy little lens), 85 f/1.8, and 135L f/2. My weakness is in the wide angle, I'd prefer the 35L f/1.4 to the 40mm, but I can't afford it, nor the 24-70 (either version) so I can't use that in it's place. If I had the money, I'd go for the 24-70 v2, 70-200 f/2.8 IS v2, and probably a couple of primes fast L primes.
Honestly, while the 24-105L is a great walking around general purpose lens, it's slow f/4 aperture really hinders it in low light, not just for the AF speed, but for needing to crank the ISO up another stop just to keep up to the f/2.8 lenses.
In terms of bodies, I don't know the Nikon side well enough, but 5d3 or 1Dx hands down. If you're making some real good money, 1Dx, otherwise 5d3. For me, the AF on the 5d3 was a huge step up from the 5d2, it's definitely changed for the better how I shoot in low light situations such as music venues or night time events.