I have EF 300mm f/2.8L IS and EF 100-400mm II.... but not 400mm f/2.8L IS (too big and heavy, instead have EF 500mm f/4L IS... I also have two EF 300mm f/4L IS lenses).
I sometimes shoot all day long hand holding the 100-400mm. It's approx. 3.5 lb. (plus about 2 lb. worth of camera and battery grip... and a second camera with a lens).
I rarely shoot with the 300mm f/2.8 hand held and only briefly when I do. With it's hood, a lens coat and an Arca-Swiss plate, it's a solid 6 lb. (so around 8 lb. with camera). I usually put it on a tripod with a gimbal head or at least a monopod. Yes, I can take a few shots with it hand held. But it gets too heavy and exhausting in pretty short order. I don't care how young or old you are.
Both lenses are extremely sharp with great color and contrast. I would say the image quality of the 300mm lens is a notch above that of the 100-400mm II. BUT, that zoom is one of the very best that anyone makes and you'll struggle to see a whole lot of difference between them (aside from the background blur and bokeh).
The 300mm f/2.8 can render much stronger background blur than the f/4.5-5.6 lens. It also renders smoother bokeh. The 100-400mm II's bokeh can be a little harsh in certain situations, such as a busy background at just the right distance. (The same is true of the EF 300mm f/4L, which is a much older optical design, pre-dating curved aperture blades and such.)
The 300mm f/2.8 is much more practical for indoor shooting.
In fact, I mostly just use the 100-400mm outdoors in reasonably good light.
When lighting isn't great, I switch to 300mm f/4 or, when necessary, 300mm f/2.8.
Between those three lenses, by far I use the 100-400mm II the most. The zoom is easily the most versatile of the three. I shoot a lot of sports. It's also great for wildlife, airshows, birds in flight... any sort of fast action. It's also my "go to" lens when hiking and wanting to keep my backpack reasonably manageable. (I do sometimes switch to the EF 300mm f/4, which is a little smaller and about 1/2 lb. lighter.) I sometimes put the 100-400mm II on a tripod, too. Especially on the occasional 8, 10 or 12 hour shooting day!
If I were going on a safari, I almost certainly would take the 100-400mm II for it's versatility. I have traveled with the 300mm f/2.8 and it's a chore.... When flying I never check my camera gear and have to carry it on. The 300mm f/2.8 takes up a lot of the available space in a backpack that's acceptable for carry-on, leaving limited space for anything else. The alternative is to ship gear ahead, which I sometimes do when I need the big lenses.
I use Canon 1.4X II teleconverter on all three lenses with excellent results. It has virtually no degrading effect on image quality on any of these lenses. On the other hand, I only use my EF 2X II teleconverter on the 300mm f/2.8 lens (and sometimes 500mm f/4), in part due to the loss of image quality on the other lenses, but also because of loss of autofocus on the 100-400mm.
Speaking of autofocus, the EF 300mm f/2.8L IS USM is very fast focusing and has little trouble tracking fast moving subjects. The 100-400mm II is slightly less quick, but also very, very good. (The 300mm f/4L is about the same.) All these lenses have Focus Limiters, but I rarely find them necessary. The 300mm f/2.8 also has means of pre-focusing and recalling that focus instantly.
The 100-400mm also is much closer focusing and able to render much higher magnification. If I recall correctly, the 300mm f/2.8 can only do about 0.16X (less than 1/6 life size). The 100-400mm II can do something in the neighborhood of 0.30X (almost 1/3 life size). I believe it's the closest focusing, highest magnification of any Canon telephotos 300mm or longer focal length.
The zoom of the 100-400mm II also has a tensioning ring the user can adjust to increase or decrease drag on the zoom ring,
The image stabilization on the 300mm f/2.8 is very good... probably about 3 stops worth. It has standard Mode 1 (correcting movement in both vertical and horizontal axis) and Mode 2/Panning (correcting movement only on the vertical axis).
The IS on the 100-400mm II is a couple generations newer... probably good for as much as 4 stops worth of assistance (though everyone's "mileage" varies). It also has Mode 1 and 2, but adds Mode 3 which is same as Mode 1, except it only activates and counteracts movement during the actual exposure. Some people prefer this to having the IS active while they are tracking a subject through the viewfinder (I prefer to keep it active).
Both 300mm f/2.8 and 100-400mm II have the type of IS that automatically shuts itself off when "on a tripod".... or in any other situation where there's no movement for it to counteract. There's usually no need for the user to turn off IS at the switch (see below). On the other hand, the older, original "push/pull" 100-400mm and the EF 300mm f/4 that I use are two of the five Canon EF lenses where it's necessary to turn off IS "when on a tripod". What happens if you forget to turn it off is that the IS can go into sort of a feedback loop where it's actually causing shake blur, when there's actually no movement for it to correct. This isn't limited to just tripods, either. It can happen in other situations when there's no movement. However, it only occurs with a few Canon lenses and you can see rapid jumping movements in the viewfinder when it happens, reminding you to turn off the IS... no real harm done.
Now, pretty much all Canon lenses with IS say to turn it off when "on a tripod" in their instruction manuals. However, Chuck Westfall, Canon USA's tech guru for many years, told me the reason for this is primarily to save a little battery power. Very little, in my opinion. I've used IS lenses for around 20 years and see very little difference in how many shots I get out of identical cameras used side by side, one with an IS lens and the other without.
There may be other instances when IS should be turned off. It's common on all lenses for it to cause a slow "image drift", which can be seen in the viewfinder (not the rapid jumping noted above). This doesn't effect image sharpness, but if shooting video or very carefully composed stills, might be a problem.
You also mentioned the EF 400mm f/2.8L lens.... A superb lens, but original IS version of it is very hefty at almost 12 lb. The 400mm f/2.8 "II" version really shaved off a lot of weight, bringing it down close to the approx. 8 lb.. of the 500mm f/4.
Other possibilities are the two versions of EF 400mm f/4 "DO" IS USM. They are very close to the same weight, a bit over 4 lb. I haven't used either, but understand that the the "II" version has better image quality and is more usable with teleconverters.
Hope this helps with your decision. Cheers!
