Not every Nikon TC is compatible with every Nikon lens - check the one you have (TC14__) to see. The reason they do this (as far as I understand) is to get as much sharpness as possible out of the lens + TC combination, unlike generic TC's. So it's not a bad thing, but you do have to have the right one.

Another thing - a 70-300 will usually be f5.6 at the long end. That aperture is at the limit of reliable autofocusing. A 1.4x TC will effectively lose one stop so it's an f8 lens and you may have problems with it. If your 80-200 is an f2.8 lens, you're obviously OK at f4.