The one f stop advantage of a bigger max aperture may not be that big a deal as it is sometimes made out to be.
It often isn't in terms of exposure in good light, and at the 200mm may not even be all that apparent in terms of depth of field.
Where f2.8 comes into it's own, particularly for sports or nature photographers - a key market for this kind of lens - is the extra AF performance.
The lens is a stop brighter, which assists AF in any case, but all EOS DSLRs from the humble T3 to the 1DX and everything in between have added AF sensitivity with an f2.8 or faster lens. In some cases this makes the difference between a point being single axis or dual axis. Do bear in mind that even if you rarely shoot wide open, at f2.8, the lens is still at f2.8 during focusing and will stop down to your selected aperture when taking the image.
I had the 200mm 2.8 II and used it primarily with an XTi (9 point AF, only one cross type - the centre) and got some really excellent results from this lens on such a basic camera (lens focus limiter is useful, Ai Servo, centre AF point) I used it briefly on my 7D and with the camera set up properly and a couple of seconds lead tracking I was getting hit rates of 8/8 at 8fps.
It's a truely excellent lens.
But my 70-200 f2.8L isn't that far behind it at 200, and gives me the 70- range as well, which is useful for my video work.
For stills only I would have the 200mm again in a heartbeat. Much faster to use, by no giving you the excuse to fiddle with the zoom, but as video is important to me I use the zoom, which I actually see as a compromise in a way.
My take: Extra aperture is big new, IS is not. For me, although I know many others disagree.