Well, the Tamron lens has quite good image quality. But so does the Canon f/4 IS... Compare for yourself:
https://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=1116&Camera=979&Sample=0&FLI=3&API=0&LensComp=404&CameraComp=979&SampleComp=0&FLIComp=3&APIComp=0One thing I really like about the Tamron.... and wish Canon would do too.... is that they incorporate an Arca-Swiss compatible dovetail into the foot of the tripod mounting ring. It's nice you don't need to buy a separate mounting plate or have any worries about it loosening.
However, the Tamron is twice the weight and about 50% larger than the Canon f/4 lens.... The Tamron also requires 77mm filters, while the Canon uses 67mm. To be f/2.8 capable requires a lens to use larger lens elements and that leads to larger overall size. Compare:
https://www.bhphotovideo.com/c/compare/Canon_EF_70-200mm_f_4L_IS_USM_Lens_vs_Tamron_SP_70-200mm_f_2.8_Di_VC_USD_G2_Lens_for_Canon_EF/BHitems/457678-USA_1317271-REGPersonally I use the same Canon lens as you quite a bit, but don't have the Tamron. So I have no idea how they compare in terms of focus speed and accuracy, though both use fast "ultrasonic" focusing motors. At least theoretically, an f/2.8 lens should perform better since most Canon cameras have one or more AF points that are higher performance when used with f/2.8 or faster lenses, not quite as high performance with "slower" lenses.
I also have no idea how the two lenses' image stabilization compares. Canon claims three to four stops worth of assistance from their IS. Tamron claims their VC is good for "up to five stops".
The Tamron uses a number of extra low dispersion (XLD) and low dispersion (LD) lens elements to achieve high image quality and has a curved 9-blade aperture to produce good background blur effects. The Canon lens uses two UD (ultra low dispersion) and one fluorite (FL) elements for similar purpose. Fluorite is both lighter in weight than glass and particularly effective minimizing chromatic aberration. But it's more expensive and difficult to work with. Canon uses it in all but one of their current and recent 70-200s, as well as many other lenses. In the last couple years Nikon has updated a lot of telephotos to use it, too. I am not aware of any other manufacturers currently using it, especially not any of the 3rd party lens manufacturers. Most have experimented with using it in a lens or two at one time or another, but AFAIK Canon is the only manufacturer to use FL extensively in their lenses since the 1970s.
You might get more detailed info about some of these factors here:
https://www.the-digital-picture.com/Reviews/Tamron-70-200mm-f-2.8-Di-VC-USD-G2-Lens.aspxVersus:
https://www.the-digital-picture.com/Reviews/Canon-EF-70-200mm-f-4.0-L-IS-USM-Lens-Review.aspxYou also might want to consider the Canon 70-200mm f/4L IS USM "II" (same price as the Tamron lens):
https://www.the-digital-picture.com/Reviews/Canon-EF-70-200mm-f-4L-IS-II-USM-Lens.aspxThe II has a 9-blade aperture, like the Tamron. And it's upgraded IS is claimed to be good for up to 5 stops. It has a number of other improvements. Announced at the same time as the Canon 70-200mm f/2.8 IS USM "III", in his review above Bryan notes that the f/2.8 lens was more like a "refresh", while the f/4 lens got more of a true "upgrade".
Comparing the original Canon f/4 lens to the new "II" version, I don't see much difference in images quality (in fact, there's not much difference between them and the Tamron, either):
https://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=1198&Camera=979&Sample=0&FLI=3&API=0&LensComp=404&CameraComp=979&SampleComp=0&FLIComp=3&APIComp=0So I think your decision is going to have to be based upon things other than IQ... size, weight and other performance factors. I'd also note that the Canon 70-200mm f/4 lenses don't come with a tripod mounting ring. It's sold separately and adds quite a bit to the cost... $149 for the OEM Canon ring for the first version lens, $165 for the new one that matches the color of the "II" lens. (They use the same "A-2" ring, but the color is different, to match the different colors of the lenses.) There are third party tripod rings for both that cost a lot less (around $50 for metal ones.... AVOID the cheaper plastic ones). How well those work, I dunno... I've used the OEM Canon ring on my lens.
I have an older version Canon 70-200mm f/2.8L IS USM lens that I used a lot for ten years or longer. It still works fine. I originally bought the 70-200mm f/4L IS USM as a backup. But now I find I actually use the f/4 lens far more often, primarily for it's smaller size and lighter weight. After all, I ain't gettin' any younger! I still get out the f/2.8 lens occasionally when shooting in low light conditions. But, for me it's become more of the backup lens.
I don't use teleconverters with either zoom. I have longer telephotos I use instead... both primes and zooms. I experimented with Canon EF 1.4X II and EF 2X II on the 70-200mm f/2.8 IS USM years ago. There was noticeable loss of IQ with the 1.4X, but images were mostly usable. The 2X, on the other hand, caused way too much loss of IQ. It was unusable on that zoom (though it was fine on 300mm and 500mm primes). I understand the newer 70-200mm f/2.8 IS USM II and III work better with teleconverters, but haven't tried them. Some examples I saw with EF 2X III on the 70-200/2.8 II seemed "okay", mostly acceptable, but my 100-400mm II and 500mm lenses are better. The relatively inexpensive and moderate size/weight EF 400mm f/5.6L USM is also excellent (too bad it doesn't have IS!)
(The 100-400mm II works surprisingly well with teleconverters. I didn't even try it for the first year after I bought the lens, assuming there'd be some loss of IQ like with other zooms. But when I finally did some test shots with the older 1.4X II teleconverter on the 100-400 II, I was stunned to see there's virtually no loss of IQ at all. It's an amazingly good combo. My 500mm prime will probably see less use!)
The 70-200mm f/4L IS USM also works quite well for portraits. I rarely use f/2.8 due to the very shallow depth of field. Working at typical portrait distances, f/4 and even f/5.6 can cause strong background blur effects. The shot below was done with the f/4 lens wide open, at 93mm focal length: