The stack used by ServerPilot is a bit more advanced than the stack used on the DigitalOcean's one-click WordPress install.
ServerPilot uses Nginx as a reverse proxy in front of Apache and uses PHP-FPM to execute PHP scripts. There's more info about this stack here:
I believe the stack used by DigitalOcean's one-click installer uses a public-facing Apache server with PHP running through the older mod_php rather than the newer PHP-FPM.
Aside from the stack configuration, the main difference is that when you use ServerPilot you can manage the server after it is created through ServerPilot's control panel without needing to SSH into your server. Things you can do through ServerPilot include creating new apps on the same server, creating additional system users, deploying Let's Encrypt SSL certificates, and changing passwords. With servers created by DigitalOcean's one-click installers, after the server is created you have to do all server administration by hand while SSH'd into the server.