I agree with anyone who says buy the 24-70mm II because it is one of if not the sharpest zoom lens available.
But only from a professional stand point, I wouldn't agree for a travel companion unless you need the extra quality for publication.
I bought the 24-105mm with my 5DMKIII which I think is brilliant and I have a stellar copy, but then bought the 24-70mm MKI because I wanted the F2.8 for weddings. I bought the MKI because I got a very late copy which was immaculate and is also a stellar copy and at the moment I don't think the double price tag for the new version is warranted although it is a brilliant lens £1600 compared to £750 easy decision. I also like the reverse zoom design, I live in Cumbria one of the wettest places in the UK and the reverse design helps keep water off the lens element 90% of the time with the lens hood being so large.
With that out of the way, I find the 24-70 stays at home unless I'm working. F2.8 isn't used very often when I'm traveling around and F4 is still great, equivalent to F2.8 on APC in terms of DOF so I don't think the OP would miss it. Also the 24-70 is lacking in range for travel photography, and it has no IS. IS is a big deal if your used to having IS on any standard lens and most standard APC lenses have it so most people will be used to it, add that to an upgrade path to a full frame camera with much more mirror slap and a heavier camera results may be disappointing. Where you are used to shooting at 1/30th-1/80th with IS you will probably find with the extra weight and mirror slap that you will end up with slightly blurred images. A learning curve with the way you shoot may be steep and annoying at first.
So in this respect I wouldn't recommend the 24-70MKII neither the 70-200mm F2.8 II. For travel purpose I would suggest the 6D with 24-105 L, 70-300mm L and a fast prime like the 35mm F2 IS or 50mm 1.4 for low light conditions.
This kit is more compact and lighter than the suggested and with weight and space a premium this is a much better all rounder than the big pro guns.
In time I would buy the 24-70MKII and 70-200mm MKII for pro shooting, you simply can't beat the combo.
Infact just buy it all
GAS will set in quick