Since the Betta is by himself the cause it most likely fin rot. Search the forum for posts on treatment and future prevention. With the amount of damage you've described, don't expect the Betta's fins to fully grow back. The most important thing is to prevent the fins from receeding any furthur.
Their are several possible reasons the guppy's fin has not regenerated. These include poor water conditions, the continued presence of fin-nipping fish, and the fact that the inital damage could have been so severe that the fin is unable to grow back.
For both these cases, the most important aid to recovery is clean water. Since the tanks in question are only 6 and 1.5 gallons, this means at least one 50% total volume water change per tank each week. In regards to possible medications, you could try Melafix for the guppy. If the Betta's fin rot is the result of a bacterial infection, and the fin recession is approaching the body, then you'll need to use an anti-biotic such as Maracyn.