Gordon, the best way to analyze this would be to decide based on what your typical shooting situation is. How often do you find yourself in low light? Are your subjects generally larger or smaller, at fairly long range or in reasonably close? You have the zoom... do you often find yourself putting a TC on the 200-400 to get the shots? How often do you find yourself at the short end of the zoom?
The 200mm is fairly short for many standard wildlife situations unless the subjects are large and in fairly close, but when the light drops (dawn, dusk, shooting into shadows) it really comes into it's own. Then, it gives you the option of giving up some subject size in the frame in exchange for at least two stops of light -- more like three stops considering the very high image quality you can get wide open. Another thing... the center of gravity is quite close to the camera with the 200mm. Along with the higher shutter speeds offered by the wider apertures, the increased focusing speed and very high focusing accuracy, this makes it possible to shoot the lens handheld very successfully. Of course, it's tricky shooting inside 20 feet even at 200mm -- DOF at f/2.8 is 4-5" at 20' and 2-2.5" at f/2 at 20'. You have to nail the focus, and you must lock on the head of your target if you're going to be satisfied with the shot.
Much of this can be said for the 300mm as well. What you're getting there is the option of gaining similar reach to that of your 200-400, less the flexibility of dropping down to 200mm, but gaining an effective two stops of light with top-quality results (the 300mm is as clean at f/2.8 as the 200-400 is at f/5-f/5.6, with a higher degree of isolation -- of course the DOF is shallower at the wider apertures but when the light drops you can keep opening up the lens). The contrast, focusing speed, and other features have been discussed above in the thread.
Now, to put my spin on your situation...
You already have the focal length flexibility. You know what a 200-400mm range looks like, and have a feel for what you can do in the f/5.6-f/8 region with that lens as well as what it will do at various focal lengths at f/4. You know what it looks like with a TC14e at f/5.6-f/8.
Consider your situation. If you're generally at the longer end of the zoom (300-400mm with occasional excursions to the 560mm range with the TC) and want easier use in the field along with the option of easy handholding, higher isolation and contrast, and aperture flexibility, the 300mm will offer you that as well as faster focusing and a higher degree of focusing accuracy in tricky situations (lower light, shooting into shadows, etc.). It works as well with the TC17e as the zoom does with the TC14e, so you'd be dealing with a 300, 420, 510 vs. a 200-400-560. You can shoot the 300/2.8VR at 510mm at f/5.6 and get very clean results. You can shoot f/5 with a slight loss in contrast and sharpness. It's a LOT easier to work with handheld, you can hike with it, you can react to rapidly-changing target locations with it more effectively due to the faster focusing (and of course the ability to handhold the lens with a high degree of success)... I'm sure you get the idea.
The 200mm offers more of the above, but with more focal length restrictions. Basically, as you know it's a 200, 280, 340mm lens (some people are willing to put a TC20e on it and accept the results -- I hated using the TC20e on the 300mm and 500mm lenses due to the loss of sharpness and contrast, and have never used one on the 200mm since I sold mine when I ordered the TC17e).
The 200mm makes a spectacular addition to the zoom to offer you the shorter range with blazingly fast focusing, unbelievably high contrast and isolation, and extreme low-light capabilities in a small, compact package (let's be honest... it's a short, stubby, very massy lens. This thing will shock you the first time you pick it up).
The 300mm offers you a little less of the above in a package that offers the same effective focal length range as your zoom (less the short end), but it's a lot easier to carry around and use in the field and you do gain a significant amount of all of the features we've been discussing. It's essentially the same sort of lens as what you have, trading off the focal length flexibility for faster focusing, better low-light capabilities, more isolation and contrast, and the ability to handhold for extended periods.
As I said, it comes down to the focal length range you work in. Do you find you have the right focal length range with the zoom, but want to gain the aperture flexibility, etc.? The answer is the 300mm. Can you live without the 400mm+ range to gain a tremendous amount of light-gathering ability along with everything else by simply removing the TC and opening the lens up (forever, it seems)? The 200mm will do that.
If this was me making the decision, I'd look at it this way: since you already have the 200-400, I'd say that it's more likely that you'd want to add the 200mm + TC14e/TC17e combination. You gain the highest degree of low-light capability and are not exactly duplicating the range you already have. If you had the 300mm, you'd find yourself going out with one or the other, and eventually you'd be asking yourself why you have both. The 200mm and 200-400VR can be used as a team effectively. That's my take, anyway. Obviously, you need to decide for yourself what makes the most sense for you.
Ron