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.
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.)