Which is the best amateur-band automatic antenna tuner made, for use
with a 160-meter inverted V with open wire feeders, to cover 160
through 6 meters?

That's a good question C.J.. I doubt that you will find anyone here that has
gotten their hands on all the automatic antenna tuners offered for sale, and
done extensive testing on a 160 meter inverted vee on 160 to 6 meters.

Also, is there much perceptible difference in performance, loss,
signal strength, etc. between the best of the best and the ones that
are only average in quality, assuming that both will properly tune the
antenna?

Once again, who would have actual experience that could report on this? Seems
like QST compared some auto tuners a while back, and there are product reviews
by users on qsl.net. These are not all inclusive.
I have several automatic and manual tuners, both commercial and homebrew that
I use in a variety of applications. The ones that work the best on an antenna
like you describe are the manual ones with the roller inductors and HV variable
caps. They will match a larger impedance range and handle power. The auto
tuners are rated for 100 watts, (except for the HB one) and have a more limited
matching range. I would make my decision based on the power handling
capability of the tuner.
Another thing, Ham antenna tuners generally don't perform well above 15
meters, with a large antenna like you have. (stray L and C in the tuner). The
radiation pattern is like a squashed spider. Be better off using a simple (and
small) dipole on 17, 12, 10 and 6m.
73 Gary N4AST