Either may "work" with cat3, but that's by no means a certainty. The twists are simply not very twisty with cat3 compared to any of its successors...and this does make a difference.
But at least: If gigabit is flaky over a given span of whatever wire, then the connection can be forced to be not-gigabit by eliminating the brown and blue pairs. Neither end will get stuck trying to make a 1000BASE-T connection with only the orange and green pairs being contiguous.
I think I even still have a couple of factory-made cat5-ish patch cords kicking around that feature only 2 pairs; the grey patch cord that came with the OG Xbox is one such contrivance. Putting one of these in at either end brings the link down to no more than 100BASE-TX without any additional work.
(Scare quotes intentional, but it may be worth trying if the wire is already there.
Disclaimers: I've made many thousands of terminations of cat3 -- it's nice and fast to work with using things like 66 blocks. I've also spent waaaaay too much time trying to troubleshoot Ethernet networks that had been made with in-situ wiring that wasn't quite cutting the mustard.)