IMO/E-regardless of tank size- if proper care is not made/done it doesn't matter....a Betta can suffer in a big tank due to poor water quality just as in a small tank...it just may take longer in larger tanks
It differs with long term and short term as well and if it is for treatment and with some Bettas the large tank(over 10gal) can even cause more stress because of the space alone, especially when they have lived in a small container for most of their life....this is all they know after all.....
Generally, if proper care is provided for the long heavy fin Betta-they may thrive best in 1-5gal long term and short term in less
Average that can give a hobbyist a margin of error...2gal regardless of filtration-however, with the experiments that I have conducted-tanks 1gal-to-4gal need the same care as far as ammonia and DOC's build-up with a single fish, average feeding and removal of left over food after feeding.....
1-4 gallon tanks: to maintain water quality
Filtered-2-50%/week
Unfiltered-1-50% and 1-100%/week
Active growth of live plants of either stem or floating will change the dynamics and water change needs to a degree......
This is based on my opinion, experience and experiments and not necessarily this forum......