nothing will be better with a TC, and then we are not talking about the advantage of the smaller pixels and resolution and the same lens.
TC also on the APS- and then?
Sorry, but that is just plain wrong. If you slap a teleconverter on a lens, regardless of what sensor you are using,
you increase the focal length. Your
OPTICAL power has improved, and now you are putting
MORE PIXELS ON THE SUBJECT. More pixels on subject is better regardless of how you achieve it. A teleconverter might introduce slight additional softening, but if it gets you significantly "closer" to your subject thanks to a greater magnification, that additional softness can't possibly be worse than having to crop significantly.
Adding a TC is valuable, be it with a low density FF or a high density APS-C....if you cannot physically get closer to your subject, you can't really do better than moving to a longer focal length. Getting closer is better, but it is not always an option, and when it is not an option, a teleconverter is often the cheapest, if not the only, option for increasing the size of your subject relative to the frame.
As a simple example, I'd happily go with a 300mm f/4 L IS + 1.4x TC rather than a 400mm f/5.6 L. Not because the 300mm has IS, but because with a 1.4x TC you get 420mm out of it. The extra focal length will offset the slight drop in IQ...you'll get more pixels on subject, not a lot, but enough to be useful, with the subject being 10% larger in the frame. Plus...you still have the IS, so its still better all around than the 400mm f/5.6 L as you won't also have softening due to camera shake. Similarly, I'd take a 600mm f/4 L + 1.4x TC on a 7D any day over the 800mm f/5.6 L on a 5D III...the 600/1.4/7D combo will pack on far more pixels than the 5D III setup. (As soon as f/8 AF is available on the 5D III, my sentiments there will likely change...600mm + 2x TC + 5D III would then become a better 1200mm setup with superior AF.)