Battlegrounds are in every realm. And I'm not sure if you can do that on normal, and it's not like it happens on PvP often either. There simply isn't enough rewards if you actually go and kill people in the capital....In fact don't they punish you for killing the npcs? Anyways, I think capitals are off-limits on every server type except if you're flagged.
If you're looking for a good PvP experience, stay the hell away from WoW.