The problem with playing the bad guys in Jason and the Argonauts is that there are no re-occurring villains, except maybe the Colchians. By its very nature, the story of Jason involves one side moving from location to location, so while the Argonaut player would get to build his Argonauts, the buy guy would need to play different monsters, baddies, each time.
One-on-one works fine for one-off games of Jason and the Argonauts, but if you want any kind of campaign system, playing bad guy is going to be tough.