Don't flip a coin... if you initiated the project, make sure yours comes first, and then the other "in association with"... You wanna be careful with "partnerships" because in the (unlikely, yet possible) event that there is a dispute over ownership down the line, the partner might be able to stop you from owning/selling/finishing your film.
It sounds like you've got a prod.co of one, and the other prod.co is also an army of one... If you're initiating the project, I'd suggest just "hiring" the other guy as a role (director/producer/editor/DoP, etc) on the crew, instead of combining prod/cos... just to stay on the safe side. If he insists on having his prod.co listed, go for it, but either a) talk to an entertainment lawyer OR b) be prepared for trouble if the other party decides at any point that he wants out, and he's taking the credit with him!