I will agree with the bigger isn't better with a betta. The most important thing to remember is that bettas breath air from the surface. This is one reason we can get away without a filter, they don't need the oxygen content in the water the way other fish do. Bettas also stress badly if not in a decorated tank, or if the tank is too big... and filters also tend to stress them out. Most bettas in a tank with a filter will hide constantly behind the intake tube and refuse to come out, even for food. They get sick this way very quickly.
The 1 gallon tank should do him fine, but I would add decorations and keep up on the water changes. Watch the temp, although they are known for survival in "room temp" water, everyone's idea of room temp can be a bit different. To be more accurate, bettas do well from 70 - 90 degrees fahrenheit. If room temp falls below 70, they tend to get sick. A sick betta in a tall tank means a betta that can easily suffocate because it can't get to the surface for air. Sadly enough, I've seen this happen too many times. It's not a pretty sight.
I have been keeping and breeding bettas for over 8 years now, and have tried many different environments. I have always had the best of luck with 2 - 5 gallons, anything larger and they seem to get too stressed. I surely wouldn't work with more than 10 gallons.
Hope this helps!