Christmas Hamster is 100% correct.No matter how big the tank and how well they seem to get along.They will fight and both could end up hurt and/or died.Only female bettas can live together and even they will sometimes have fights.But alot of people on the betta forum I visit have great female comminty tanks.If I remember correctly Christmas Hamster is one of them.
If you think your other betta is mopey maybe you could put a mirror by his tank for a few mins.each day and let him have fun flaring or get him a new plant or decoration.