I'm a firm believer that most 'tank size' bettas simply have had a hard time overcoming swimming room + lighting adjustments that follow.
I think almost any betta can be happy in a 5+gallon provided s/he is provided with:
-- adequate hiding spots that correspond to the size of the tank (a 1 gal will need fewer hidey holes than a 5gal)
-- adequate lighting adjustments: most of us change lights when we change tanks, and I think we underestimate how much that affects the fish. Provide a few floating plants (like anacharis or java moss) and see if that helps.
I personally think it is worth keeping individuals in 5+ tanks, simply because it allows for greater stability in water params. I think most 'larger tank' issues can be adjusted for by adding differing quantities of live plants to provide stability + shelter.
That said, not everyone digs live plants. If you don't, I'd recommend keeping him in the tank that he seems happiest in.