Ed:
   The OP doesn't describe his 80-200 as an AF-S version, therefore he will
lose auto-focus with any of the Nikkor converters.  The TC-20, TC-17 and the
TC-14 auto-focus only with the AF-S lenses and the TC-200 or TC-201 don't
auto-focus with any lenses.  I think his only recourse is Kenko or another
off-brand if he is using the in-body focusing motor type of 80-200mm lens.
Bob

There are mainly three areas in which teleconverters differ (with
specific reference to use with a Nikon DSLR):

1) multiplying factor. This is usually 1.4x, 1.5x, 1.7x and 2x. This
controls by how much the focal length of the lens is multiplied. In
practice, the higher this factor, the higher the degradation of the
images shor with the TC. This factor also affects how many stops you
lose (1 with a 1.4x TC, 2 with a 2x TC). With a Nikon DSLR, you are
going to lose autofocus if the effective speed of the lens + TC is
slower than f/5.6 (although this may vary somewhat). Usually, 1.4-1.5x
produce good results, while 2x gives a noticeable degradation of the
image (but this is also affected by the quality of the lense).

2) optical quality and design. Some TCs (e.g., Kenko) are designed to
fit any lense, while others (e.g., Sigma) have a protruding front
element that prevent them from mounting on some (usually shorter FL)
lenses. TCs may also be designed to work best with short-medium teles
(Kenko) or long teles (Sigma, Nikon). While all popular TCs nowadays
have a rather good optical quality, they will perform best with the
specific range of FLs (and sometimes lense brands) for which they are
designed.

3) AF couplings. Nikon uses two: the mechanical "screwdriver"
connection and the electronic one. Kenko (and Tamron?) TCs provide
both, but Nikon and Sigma only the electronic one. Both types of AF
usually work slower with a TC.

With very few exceptions (e.g., the Sigma 300-800 and the Nikkor 300
f/4 seem to be so sharp to start with that the following argument does
not apply), any TC will introduce enough image degradation to produce
visibly worse results than using a longer FL lense without TC. So a TC
is a way to save money and/or carrying weight, but it is always a
compromise with image quality. In the worse cases, cropping an image
taken without a TC may give better results than using a TC.

In your situation, I would choose a Nikon 1.4-1.7x TC if your Nikkor
lense has electronic AF.