Should i play lefty or righty guitar?

I've been playing guitar for about 1 year now, and I am not really sure what hand I should play. I am a natural born lefty playing a righty and when I play the righty way my fretting hand has no problem but it seems that my picking hand can never reach the precision that my left hand has when I flip the guitar over....the catch is tho when I flip the guitar to the lefty side my fretting hand feels awkward and cannot move as well on the fretboard as it did when it was played righty....any advice on this? I will say that as i practiced more my right picking hand has improved but i guess it just dosent seem that it will ever get to appropriate speed or have the precision as my left does.....