As someone who's shot well over 100K frames with an EF 24-105mm f/4L IS on EOS 5D Mark II and 5D Mark III bodies, as well as a large number of frames with an EF 24-70mm f/2.8L (original version) over the past decade, I'm going to buck what seems to be the prevailing wisdom here and say you should seriously consider the Tamron SP 24-70mm f/2.8 Di VC G2. The G2 stands for Generation Two (both generations of the Tamron SP 24-70mm f/2.8 Di VC use the same optical formula - the G2 has more advanced lens coatings to reduce internal reflections and flare as well as some non-optical improvements that are also well worth the upgrade). If I needed to buy such a lens today, I certainly would put it at the top of my list.
- The previous Tamron SP 24-70mm f/2.8 Di VC gives the Canon "II" a good run for its money.¹ At f/4 and narrower, there's virtually no difference in sharpness between these two lenses at any focal length and aperture. At f/2.8 they're both about the same at 24mm and the Canon EF 24-70mm f/2.8L II pulls away a bit as the focal length increases to 70mm. But the Tamron vignettes less, distorts less, and shows less chromatic aberration wide open at f/2.8 (particularly at 35mm and 50mm) than the Canon does. Is the Canon EF 24-70mm f/2.8L II sharper across the zoom range from 35-70mm at f/2.8? Yes it is. But not by a whole lot. They're both very good and significantly better than the older Canon 24-70/2.8L or the EF 24-105mm f/4L IS.
- The previous Tamron is a lot closer to the very good Canon 24-70/2.8 II than to the older less sharp original Canon EF 24-70mm f//2.8L, which I still use. The old Canon 24-70/2.8 is plenty sharp for your stated use cases. It's also noticeably sharper than the EF 24-105mm f/4L IS when camera movement is not a concern. Both generations of Tamron's 24-70mm f/2.8 Di VC lenses are sharper than the older Canon 24-70/2.8, and even more so than the EF 24-105mm f/4L IS.
- It has Vibration Control, which is Tamron's name for IS. One reason (among several) that I tend to use my 24-105/4 more than the 24-70/2.8 is because of IS. There are situations where IS is worth more than an extra stop of aperture. There are situations where an extra stop of aperture is worth more than IS. I tend to shoot more of the former (i.e. standing on a vibrating temporary outdoor concert stage) than the latter, but when the camera is on a tripod my 24-105/4 is rarely on it and the 24-70/2.8 often is.
- The EF 24-105mm f/4L IS is legendary for it's toughness. It is one of those lenses that takes a beating day in and day out and just keeps on working. (The older Canon 24-70/2.8, on the other hand, does not. The EF 24-70mm f/2.8L II is a totally new design that corrected the issue that was the older version's Achilles heel.) But the Tamron SP 24-70mm f/2.8 Di VC also has developed a reputation for being a good workhorse lens.
I know a shooter who is a helicopter based flight paramedic in the U.S. Army while also pursuing a degree in photography. One of his major projects for his degree program is a photographic study of the various helicopter mounted units with which he has served and currently serves. From combat deployment in the Middle East to environmental extremes in places such as the California and Nevada deserts around Death Valley in the summer to Alaska and upstate New York in the winter, his Tamron SP 24-70mm f/2.8 Di VC has often ridden along with him in the high vibration environment of military helicopters. He also likes to take his camera along for a bit of off-road travelling in his personally owned Jeep. I've asked him several times since he got it shortly after it was introduced back in 2012 how it is holding up and every time he has said it's still as good as the day he got it.
Lens choices can be intensely personal decisions. What is the "best" lens for one person may not always be the best choice for another. It may well be that you would prefer the extra "reach" of the EF 24-105mm f/4L IS (or the newer IS II - there's not much difference between them performance-wise) over the larger aperture of a 24-70mm f/2.8. The slightly lower image quality of the current 24-105mm f/4 lenses compared to the current state of the art 24-70mm f/2.8 lenses may not make that much of a difference for you.
One thing I would advise, based on your apparent experience level from what you've told us in the question, is that you should probably consider a stabilized lens, whether f/2.8 or f/4. For a more casual, less experienced photographer I think IS is more significant than for a seasoned pro who has plenty of other tricks up their sleeve if need be. Especially since you can have both IS and f/2.8 in a 24-70mm lens from Tamron or Sigma (though I think the Tamron is better optically). This is particularly the case when you're already moving from a crop body to a FF camera and considering lenses with wider apertures than your previous one. The narrower depth of field a larger sensor and a wider aperture will yield often requires improvement in technique. Some forms of poor technique that you might have gotten away with using an APS-C camera at f/5.6 will be more noticeable with a FF camera at f/2.8. You probably don't also need to be moving from a stabilized to a non-stabilized lens at the same time.
¹ As always, "composite scores" at DxO Mark should be taken with a grain of salt. How DxO weighs various factors, which they don't reveal, may be different than how a particular photographer might weigh each of those same factors. Click on [Measurements → Sharpness → Profiles] and then start playing around with various focal length and aperture combinations to see how actual measurements of the two lenses compare in various setups. You can do the same with the other categories: Transmission, Distortion (Profiles), Vignetting (Profiles), and Chromatic Aberration (Profiles).
Why does it seem you've shot so many more frames with 24-105/4 than with 24-70/2.8, yet recommend 24-70/2.8?
- As I said above" I tend to shoot more of the former (i.e. standing on a vibrating temporary outdoor concert stage) than the latter. Much of the time IS with f/4 makes more sense for what I am shooting than f/2.8 without IS. The Tamron SP 24-70mm f/2.8 Di VC G2 gives both options in the same lens.
- Because of the vulnerability of the original 24-70/2.8 to misalignment from relative minor bumps to the front of the lens combined with much of my work involving being in crowded places where such bumps are likely to occur. Neither the Canon EF 24-70mm f/2.8L II nor the Tamron SP 24-70mm f/2.8 Di VC G2 suffer from this same vulnerability.
- I already owned both the EF 24-105mm f/2.8L IS and the EF 24-70mm f/2.8L before the Tamron SP 24-70mm f/2.8 Di VC was introduced. They're still good enough for what I do. I've chosen to spend available resources in other areas rather than replace the two older Canon lenses with the newer Tamron.
If the Tamron with VC had been available when I bought the older Canon 24-105/4 IS, I'd have bought the Tamron instead - hands down. I would then not have even needed to consider spending even more for the EF 24-70mm f/2.8 for a few specific use cases where it can get shots that the EF 24-105mm f/4L IS can not.
A lot of the images I've shot with the EF 24-105mm f/4L IS since 2012 would have been shot with the SP 24-70mm f/2.8 Di VC instead. In fact, almost all of the images I've shot with either the 24-105/4 or the 24-70/2.8 since 2012 (when the Tamron was introduced) would have been shot with a Tamron SP 24-70mm f/2.8 Di VC had I owned one. The only reason I'm not using the Tamron is because it was not available at the time I made my lens purchases. Instead of having to choose between f/2.8 with one lens or IS with the other, the Tamron gives both in the same lens while also being better optically than either one. It's also cheaper than what I paid for either of the other two.