They don't cancel each other. This can be easily seen by looking at the server log messages of the damage dealt, which will still show the note about the increased damage:
20:34:18 Ferumbras loses 3368 hitpoints due to a critical attack by <player>. (active elemental amplification)
20:34:18 Ferumbras loses 2826 hitpoints due to a critical attack by <player>. (active elemental amplification)
20:34:18 Ferumbras loses 2762 hitpoints due to a critical attack by <player>. (active elemental amplification)
20:34:20 Ferumbras loses 3082 hitpoints due to a critical attack by <player>. (active elemental amplification)
The message above is a real message from Ferumbras on Pacera a few days ago, showing the damage dealt by the player who dealt more damage to the boss and won Ferumbras' Hat. Obviously, he had Avatar on.