We use both f/4 and f/2.8 300's in our pro shooting. Nikon rather than Canon, but I can add perspectives from long-term use of both.
In a nutshell, the f/2.8 is a PITA compared to the f/4 when you are traveling or spending long days with your gear hanging from your shoulder. Terrific lens it might be, but it's much larger and heavier than the f/4. You'll often find yourself leaving it home, while you'll often carry an f/4.
The only time the f/2.8 really shines and justifies itself is for shallow DOF shooting. If you do a lot of that, then you'll put up with the extra weight and bulk. We do probably 2/3 of our outdoor model shoots with the f/2.8, finding it provides a superb combo of shallow DOF and perspective.
In that light, the 200 f/2.8 might serve you well. When really pressed to limit our loads we often simply carry our 80-200 f/2.8's for portraits and a 1.4 converter for a little more reach.
It all boils down to weighing your uses against weight, bulk and expense. In our case there are ample reasons to own both, but I'd sure hate to have only the 300 f/2.8.
