I would think, given normal GA speeds, the one on late downwind, about to turn base, would reach short final a lot sooner than the one of a 3nm final.
Also, the one at 3nm will have a much better view of the traffic (including the traffic on downwind/base) than the one on base because the latter cannot see so well to the right, and somebody descending on a 3mile final will have a super view of the whole circuit and surrounding area.
LH circuits assumed.
This business where the one on final has the right of way sometimes results in people telling porkies about where they really are...
This is the problem with flying a long final. It is an attractive way to arrive if you are flying a programmed route (GPS etc) so you are all set up, altitudes/speeds etc, long before you see the airport, but it can result in you having to do repeated go-arounds. Still, IMV, it is safer than joining a really busy circuit from any side position, or from the overhead.