How are you dividing the tank? Because if you're using a straight up sheet of acrylic or whatever then theoretically you're going to have to filter both sides of the tank, and unless you're using some sort of mesh or net, you're going to have to buy double the filters and probably heaters too. Not exactly low budget. It's a nice idea, but im considering whether it would be worth it for you in the long run. If you really want two male bettas, why not just add one betta to this 10 gallon with a few other fish, the buy a seperate little nano for the other betta.
Good luck anyhow!