A 20g can handle a vacation feeder much easier than anything under 5g.
As for the automatic.. I've heard mixed reviews -a lot of people saying it malfunctioned and either didn't feed, or went around and fed all at once.
It's up to you if you want to risk fouling up the water and possibly causing over eating. Personally since a betta can go weeks without food with no ill side effects if the fish is healthy, and water quality is the most important thing while you're away.. I rather risk it then try to feed them. But that is my preference.
Wish you luck with whatever you decide.