From personal experience: PostgreSQL's COPY commands aren't really all that performant, indexes or no.

Our project saw SIGNIFICANTLY better performance with batched multi-threaded INSERTs. If you can run a few hundred load threads and manage the concurrency correctly (not trivial), it will chew through big loads like a monster.

If I ever have the time/excuse, I want to go back and try a multi-threaded COPY. But if you need speed and have a choice between multi-threaded INSERTs or a single-threaded COPY, go with the INSERTs every time.