A 300/2.8 is a big, heavy lens, but it produces VERY nice background defocus, and very strong seapration of the subject from the background, at typical "sports distances". All of Canon's 300/2.8 lenses have had TOP-grade optics. The issue though is heaviness, and the fact that much of the time, it leads to cliche type shots: when a player is close to you, you MUST cut off their lower body parts...there's just no other thing you can do. Which leads to cliche sports photos, the kind we see so much becasue so many are shot with a 300/2.8. You know....legless running back bursting through the line...etc, running with no hips,no legs,no feet, just the top part of their body... Seemingly though, pro sports shooters seem to ignore that their work has become pretty cliche'd, as they keep cranking out these half-body and third-body, context-free photos day in and day out.
The TECHNICAL image quality of photos made with a 300/2.8 is high. Buuuuut....indoors at a volleyball match or a basketball game, or in many situations where you have no place to be except in designated press spots and you are stuck in one, small location, you have to have some OTHER lens in order to get a lot of shots you really want to come back with, meaning you need to have a wider-angle option with you, on a second body, ready to make a lot of closer-distance shots. Sometimes though, a 300 is exactly what you want!
You ask if it is a "huge difference in IQ". Well, not huge quality leaps, but a very different "look" to the photos. The 300/2.8 is a PITA to carry unless you use it a lot, and are fit, and it works great. But new 70-200/2.8 lenses are now, very,very good optically. And they allow you to zoom-back when needed, and to show different types of things, whereas the 300mm prime is more of a one-trick pony.
100-400 f/4.5~5.6, apparently the NEW one is better than the old trombone model, but it is still "slow" in f/stop, so it's going to create different-looking photos. You've been asking a lot about gear options, so you might really like to rent the 300/2.8 before committing to it. And consider the 300mm f/4 as a viable option, now that Higher-ISO Canons are everywhere. I sold my 300/2.8 AFS-II this past summer, and kept my 300/4 AF-S. it's lighter, and easier to carry than the 2.8 model.