<<Other than the fact that the copper nuts are self-locking and
stainless aren't, is there any reason one is preferrable over the other
for the exhaust system? How about stainless vs regular carbon steel for
the bolts into the head?>>

Copper nuts are Ok for the nuts to the head flanges .
I just loaded up with stainless hardware simply because if I ever wanted
to re-do anything in the exhaust system / head area, it'l all come loose
without as much effort.

I'd stay away from carbon steel studs / bolts to the head.
Electrolosis is the main problem.
Steel to aluminum is a bad deal.