Versatility & Tradeoffs
A lot of arguments for the 70-200mm at the moment, so I feel good about providing my own counter opinion. I don't deny that the 70-200mm lenses, in all their variants, are excellent lenses. There is also something to be said about versatility, and the 70-200mm definitely has that. There are drawbacks to it as well, and there are certain tradeoffs that the 70-200mm lens (or any zoom lens for that matter) has to make in order to offer that kind of versatility.
The Excellent 300/4
As a bird and wildlife photographer myself who has recently tried the EF 300mm f/4 lens, I have to state that it is an excellent lens! From an IQ standpoint, since it can be optimized for a single focal length, it is superb. It is not the fastest lens at f/4, it is more middle-ground...but it is better than f/5.6. Since it's IQ is so high, you also have the option of safely adding the EF 1.4x TC III to extend the lens to 420mm f/5.6 when you do need extra reach. Combined with an APS-C body, you get extended reach.
The wide aperture at that focal length also helps produce a very nice, pleasing out of focus background, and since background blur is dependent on entrance pupil, boke remains high quality even with a 1.4x TC attached. This would be a key benefit over the 70-200, which while it has the same relative aperture, its entrance pupil is smaller, thus reducing the maximum amount of blur. The longer focal length of the 300mm also helps produce a thinner DOF, which can be key to isolating your subjects.
Safari and the Vaunted Supertelephotos
If you are indeed going on a trip to Africa and intend to go on a Safari, then even a 300mm f/4 with a 1.4x TC for 420mm is probably going to end up leaving you a bit short in many circumstances. As a "Next lens purchase" option, you really can't go wrong with either the 70-200mm or 300mm lenses. I would recommend either, or both, depending on your general usage patterns and funds. Personally I have found that I rarely actually zoom when photographing birds or wildlife. Both tend to stay or simply be far enough away that if I need to change my composition, I move myself and just stay at the longest focal length...or use a prime. You have the added benefit of improved IQ and near-perfect IQ at maximum aperture with prime lenses, something that is rarely the case with zoom lenses (although there are a couple exceptions.)
If you are really intending to go on a Safari to Africa, I'd pick up the 300mm f/4 as your next lens purchase, but also bring along a supertelephoto rental as a backup. Either the 500mm f/4 or 600mm f/4 are both excellent options. You might choose the 500mm if you intend to only photograph the wildlife, or the 600mm if you want to photograph birds as well. The 500mm with a 1.4x TC becomes a 700mm f/5.6 lens, which gives you a pretty broad range of focal lengths with two lenses and a single TC: 300mm, 420mm, 500mm, 700mm, at apertures of f/4 and f/5.6. The HUGE entrance pupil of the 500mm lens also brings the added benefit of fantastic background blur and a thin DOF, which will really help you add that extra professional touch to your wildlife photographs.
If you also want to do some bird photography while you are there (and there are a number of species unique to the African wilderness), I'd recommend renting the EF 600mm f/4 rather than the 500mm. The extra reach, which with a 1.4x TC becomes 840mm, could be essential for getting quality bird photographs from your Safari vehicle. It could also help you get some close-up facial portraits of the more dangerous creatures such as Lions and Hyena. The 600mm f/4 lens from Canon sports their largest entrance pupil at 150mm, giving it the most power to create incredibly pleasing, creamy smooth OOF background boke. Subject isolation, either for birds or wildlife, won't be a problem with this lens, even at great distances or when paired with the 1.4x TC.
If you have the benefit of getting really close to your subjects, having the 300mm on hand would be a huge bonus, as a longer lens at 500mm or 600mm could preclude getting good composition on shots of closer subjects. The 300mm lens is a great addition to ones kit, especially for domestic wildlife, and is an excellent focal length for such endeavors giving the lens use over a long life. However if I were to go on an African safari, I would be loath to go without some real telephoto power in my backpack. A lot of wildlife frequently stays at a distance, and a lot of the best photos are taken at a distance where the wildlife can pay attention to their normal activities, rather than to the photographer or the vehicle they are romping around in...offering better opportunities for natural shots.
Rental for either the EF 500mm or EF 600mm lenses (the older generation) are relatively cheap...rolling in at around $300 per 5-day rental period ($660 for the 500mm f/4 for a full two weeks, with return on the Monday following those two weeks, from LensRentals.com.) If you have the funds, the newer Mark II versions of these lenses are considerably lighter than their older cousins, and bring to the table true supertelephoto hand-holdability in a pinch. They are considerably more expensive to rent, at almost twice the cost...but there are no better lenses on planet earth from a weight, IQ, and reach standpoint. Safaris don't roll around all that often and tend to be expensive regardless, and when 300mm or 420mm just isn't enough to get your half-decent shots of distant animals, you'll probably be wishing you dragged along that 500mm lens, even if it costs you an extra $800 for a few weeks.
Regarding APS-C Reach Benefit
Using the most common terms, you can apply the crop factor, 1.6x, making the 300mm/+1.4x lens like a 480mm/672mm lens on FF. The actual reach benefit really depends on pixel density differences, but in most cases when comparing to 18-22mm FF sensors the gains are around 2x or more (i.e. for every one pixel in the 1D X, the 7D offers 2.6x pixels in the same area, or 2.3x more pixels than a 5D III).