I'm on the opposite side of the fence, so to speak. I bought my 24-105 and used it for a couple of months before I picked up the 24-70. Although the extra stop was nice to have on the 24-70, the added weight and lack of IS resulted in less than great results for the bulk of my low-light shooting at church. I'm at the point of selling the 24-70 in the not too distant future. Not because of any problems, but I like the 24-105 better.
Also, as you already have the 70-200, staying with the 24-105 provides a comfortable 35mm focal length 'overlap' between lenses. I prefer the overlap to avoid 'forced' lens changes right at 70. That way, if I need a little length at 70, I have it, and on the other side, if I need a little wider than 105 on my 80-200, I have that, too. All without a lens swap. On the other hand, having 2 bodies would seemingly alleviate the 'forced swap'. However, putting down one camera and picking up the other might lose 'the moment' that could have been zoomed into almost instantly.