Browd's explanation is complete and precise.
Note that you can find simple mods to remove or raise the XP-from-barbarians cap. They're fun to try out. (Getting a bit off-topic here ... you may know this stuff, just typing for fun.)
They raise some other issues, though. (1) The player and the AIs both get combat bonuses vs. barbs -- the bonuses vary by difficult level, and they can get really high. (2) raging barbs = raging promos? (3) The AIs units often behave oddly, for ex., standing in heal mode near an archer, taking arrow hit after hit, without responding for what seems like an eternity.
So my main point is that you might enjoy a barb XP mod, but that the game settings will determine what sort of experience you have.