Which lens is sharper with TC-20E III: 70-200mm f/2.8 VRII or 70-200mm f/4 on D800/E

What is wrong with using a 1.7x teleconverter with the 70-200? I have read many users talking up the awesome image quality of this combo. It's almost as though the 1.7x was made for the 70-200, it is that good. And wide-open aperture is f4.8 (lose 1.5 stops of light).

I would personally prefer the versatility of the zoom lens over the fixed 300, but that's just me.

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K.B.