I think your betta will do just fine in any tank, the important part is that it has clean and warm water. If find Bettas are generally much healthier and disease resistant in temps around 80F.
The main advantage to you larger tank is the fact that the water quality will be much better simply due to the larger water volume. It will take more time for the water to deteriorate and should give enough time for the nitrogen cycle to establish itself.
Super glad to hear you are housing your bettas in appropriate sized tanks. Good luck!