The point in question is whether the Tamron or Canon is preferred, ceteris paribus.
I believe you are. I would be surprised if it was even 10% of people who would prefer the Tamron. Let's just pretend everyone (on this forum) wins a free lens at the camera store and they have a pile of Tamrons and a pile of Canons. I really really really doubt that given the choice, very many people are going to walk out with the Tamron. Because I deal with contracts and by nature, "paranoid", I would even say that the choice would not change much if you told them they could not sell the lens.
The point I am making is that I believe the 2 canons are the best but the tamron is very close behind and will give you undiferentiaded results under most conditions so anyone on a budget should take a good look at it.
Anyone on a budget doesn't have a choice but to choose the Tamron. Someone with (truly) the budget, is going to pick the Canon (nine times out of 10).
In that case I must be in a minority of 1 out 10. If you have the strength and like using monopods or tripods then go for the Canons if you have the cash - you will get the ultimate quality. But, if you want to use hand held and like a light package for hiking and birds in flight etc, then those great lenses are just too heavy. I could not handle them. I would rush out and buy a Canon 200-500 f/5.6 that beats the Tamron, and pay the price.
You might as well ask suppose somebody offered you a 100 carat diamond studded solid gold mounted Sigma 50-500 or a plain Canon, which one would they take? That situation is just as unlikely as everyone on this forum being offered what you would suggest. If I was given a 200-400mm Canon I would never use it. And that is a fact, not a let's pretend scenario. But, if someone were to offer me a 200-400mm free of charge, I would of course accept it - that is human nature.
The only reasons I can imagine for buying the Tamron over the Canon are price and weight/size. You already said you don't want a big lens so you've explained that your utility formula places a higher value on size/weight. Because this forum is full of gearheads and guys who care about IQ, I still believe that at least 90% of those on this forum would choose the Canon over the Tamron if they could afford it.
You can go buy the Tamron.
As someone else wrote, it would be more sensible to have discussion on the 300 vs the 200-400 as they overlap in focal length and the 600mm is for a different purpose. I made the decision to buy the 300mm f/2.8 II plus extenders because I care about both IQ and weight.
There is very little to choose between them in IQ. But, the 300 weighs 1.27 kg (2.8 lb) less. At 300mm it gives a stop wider aperture and better IQ at f/2.8 than the 200-400 at f/4 – see:http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=764&Camera=453&Sample=0&FLI=2&API=0&LensComp=739&CameraComp=0&FLIComp=0&APIComp=0
At 420mm and f/4 it is nearly as good as the 200-400mm at f/4.http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=764&Camera=453&Sample=0&FLI=4&API=0&LensComp=739&CameraComp=453&SampleComp=0&FLIComp=1&APIComp=2
At 600mm, it is slightly better than the 200-400 at 560mm with the in-built TC at f/5.6.http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=764&Camera=453&Sample=0&FLI=5&API=1&LensComp=739&CameraComp=453&SampleComp=0&FLIComp=2&APIComp=1
Whereas I would never use the 200-400, I could see myself using the 600 with a 1.4xTC on the rare occasion I wanted to sit in a hide for a day, not too far from my car. So, I would take up the offer on a free 600mm.
You can go on a hike with your arm wrenching 200-400 while I will jauntily carry my 300mm as I am more concerned with celeris than ceteris.