what will it give me that the 70/300mm wont ?
The biggest difference is the maximum aperture. There is a big difference between F2.8 and F5.6, two whole stops (4 times as much light).
So if you are shooting in less than ideal light, it may be hard to get fast enough shutter speeds with something like the 70-300mm. IS does help to combat camera shake and give you less blur...but it won't help when your subjects are moving. Only a faster shutter speed will help, and having a larger maximum aperture is the key to faster shutter speeds.
Of course, you can also turn up the ISO to get faster shutter speeds...but that introduces noise.
Also, a larger aperture allows you to get a shallower DOF, which can be especially good for isolating a subject from the background.
I have the 70-200mm F2.8 L IS, and it's my favorite portrait lens.
Also, the 70-200mm is an
L lens...meaning that it's a top of the line Canon lens and as such, has great image quality. The 70-300mm IS, is pretty good (and much better than the other 70-300mm lenses) but it's no L lens. Plus, there is some prestige associated with L lenses. They have the red ring on the front and the one in question is one of the large white lenses that will certainly garner some attention when you are using it.
On the flip some, maybe you don't want that kind of attention. Also, the 70-200mm F2.8 L IS, is a big, heavy lens. I don't even wear the camera strap around my neck when using this lens....I either hold it in my hand or use an extra long strap and put it across my chest/shoulder.