Hello, I have used both and I now use the Wireguard app. There are both pros and cons.
Both are available on Playstore and F-droid, that is great. Wireguard app is quite barebones and lightweight but on purpose. To use the Wireguard app you need to generate configs on the Mullvad website and import them manually, but I think there is a QR scanner feature that makes importing configs easy (so no need to transfer files to your phone - just scan a QR code and the config is imported). Personally I generated a couple of Mullvad configs: one Swiss, one Swedish, one Multihop. But with these configs you are stuck on the server that you selected when generating the configuration. Generally if you are using VPN just for privacy, you don't really need all the servers and countries that Mullvad offers, just a few configurations that work for you. Another bonus of the Wireguard app is that you can also import other (non-Mullvad) configs: I have actually managed to set up a Wireguard VPN for my home network and a Wireguard VPN for me and my coworkers. Once you get these up, they are super reliable and Wireguard is a superior protocol to OpenVPN.
What you get with the Mullvad app: an app that is really easy to use but a bit bloated (personally I don't need a fancy UI that shows me where I am connected to on a map of the world). But you can choose countries and servers at will. Tired of Switzerland and suddenly want to pretend you are in Romania? Just click on the map and it "just works". If you were using the official Wireguard app, you'd first have to visit the mullvad website, generate a new romanian config with a specific server, import that into the app, etc. But with the Mullvad app you are stuck using Mullvad, you can't import any 3rd party configurations.
Both +: Open-source apps, available on Playstore and F-droid, reliable
Mullvad +: Ease of use, instant freedom of choosing every country& server Mullvad offers
Mullvad -: A bit bloated, locked to Mullvad servers
Wireguard +: Lightweight, not locked to Mullvad: can import 3rd party configs
Wireguard -: Not so intuitive, have to generate separate configs on Mullvad.com and import them
Hey, and also, if you are interested in setting up a Wireguard VPN to your home network (a strong recommendation is a static IP from your ISP), I can give you some suggestions if you ask.