OK, from experiments run by me and another much lower player:
Battles against players of EQUAL level will result in 5 XP for the loser and 20 XP for the winner.

The lower player losing to me gave them 5 XP and 4 XP for me.

When I did a bunch of wins in a row: Average XP for me was 16.8 each. Those were mostly battles against people within 2 levels of my own.