It has more features. Check https://apps.apple.com/us/app/amphetamine/id937984704?mt=12 for details.
The one you linked to looks like a simple wrapper of caffeinate(8).
Caffeine might be better in this scenario, but amphetamine has some auto triggers and custom settings for keeping the system awake but still turning off the screen, etc.
One difference is that Amphetamine isn't updated as well, also seems more hackish. I switched to Caffeine a while ago.
Re:I think Catalina 10.15.4 broke SSH
by blacksmith_tb on Tuesday March 31, 2020 @01:26PM
(#22739939)
Or just running caffeinate -t 10000?
http://lightheadsw.com/caffeine/