The completion of objectives get you experience. Along with winning in the end.

As a boxer, taking a tower/bunker and ensuring it burns. Then taking the next tower/bunker and doing the same. Possibly killing Galv/Belinda in there too, is probably the best way to earn experience.

As far as winning, retaking your tower/bunker so it does not burn, is a decent plan too. A bunker is much easier to maneuver your way up, then the towers. So alliance might be better off defending their bunkers and horde might be better off holding/burning the alliance bunkers.

I wouldn't want to Battleground as my only source of experience. But it is definitely a change of pace, from a monotonous grind. Mix it up, you have Battlegrounds, Dungeons, Quests and Mindless Killing as the basic leveling tools.