From what I gather, it seems to only be some sort of joking love/hate relationship, like a lot of the commonwealth countries have. I believe this trope is relevant:
http://tvtropes.org/pmwiki/pmwiki.php/Main/VitriolicBestBuds
Though, I will say I don't quite get the accent thing. Maybe its because im on the literal other side of the world, but I can't tell the difference between your (silly) accents. But hey, it could just be me. I couldn't tell you a New Zealander out from a crowd or anything.
http://tvtropes.org/pmwiki/pmwiki.php/Main/VitriolicBestBuds
Though, I will say I don't quite get the accent thing. Maybe its because im on the literal other side of the world, but I can't tell the difference between your (silly) accents. But hey, it could just be me. I couldn't tell you a New Zealander out from a crowd or anything.