I own the 24-105 F4L, and it's a great lens. Good AF, and the images are amazing, crisp and clear. The reason I bought it instead of the 24-70L is I feel it's a better street lens because it gives you more range when you need it, so you don't need to carry a second lens (and a bag to put it in, and etc....). A body and a 24-105 make a good walk-around combo where you can leave everything else at home except a spare battery and some cards in your pocket.
I also own the 70-200 F2.8l IS II (and an older 70-200 F2.8L IS I plan on selling). I don't own the 70-200 F4 but there are times when I want to because the 2.8's are beasts. Amazing, amazing lenses but they aren't small. Or light. Or easy to carry. Or cheap.
The real answer here is "what are you planning on doing?" -- either lens you suggest is a good, solid lens. What really matters is what you are going to do. If your primary range is around 100mm, I'd lean towards the 70-200, but I'd stop and see what my secondary range tendency is (if you use lightroom, you can dig into the image data and see what MM images were shot at). If it tends towards the wide angle range, go for the 24-105. If you tend towards telephoto, go for the 70-200. You don't give us any real info on what you're doing so it's hard to say. I think in the 100mm range the 70-200F4 will be crisper, but it won't be a significant difference.
But also think about shooting conditions. Low light? Movement? Fast AF? If you need those things, that pushes you towards the 24-105.
Think about future upgrades. If you but the 70-200, what will you do about covering the wide angle when you need it? Are there reasons why you might want to move from the 70-200F4 to an F2.8?
Either one should serve you well. Which one you should buy (first. honestly, I think almost all photogs need to have lens coverage in the 30-200 range, which means all photogs could benefit by these two lenses, or equivalent ones) depends on where your photography goes when it leaves that primary range you're interested in. Does it go wide? Or does it go for power? That'll lean you one way or the other.