I'm also left handed and play right handed... When I first started learning, I decided to do it that way so that I wouldn't always need my own guitar and could play whatever guitar was laying around. I have found strumming and picking to be a greater challenge to get right, but the fretboard has probably been easier so I guess it balances out. And eventually my right hand started behaving itself too. 
I don't entirely understand why it'd be better to play one way or the other, since the guitar is really a two-handed instrument. Just play whichever way feels right. (When I first started, it DID feel weird to play right-handed but now it feels normal, and would feel weird to play left-handed.)