Pro apt:
- storage efficient
- may be optimized for stuff like x86_64 v3 or v4
- runs as many users and easily from terminal
- needed for some low level stuff like system packages
Contra apt:
- a ton of stuff comes from outside the main Ubuntu repo. Debian doesnt have that difference afaik but still many packages may be more abandoned
- 3rd party packaging 99% of the time, i.e. "unverified". I had a lot of strange bugs especially with Ubuntu packages
- the apps ars not isolated at all
Pro Flatpak
- a ton of verified apps, nearly unavailable on other repos (that still doesnt make unverified apps insecure!)
- all apps have a sandbox that can be graphically hardened to be more secure, if the defaults are too broad
- by defaults the sandbox is pretty good
- many many apps that run everywhere
Contra Flatpak
- not suited for some apps like terminal apps or system stuff
- some apps are less maintained and use EOL runtimes etc
- some more storage space needed
- need user namespaces, nearly all distros have them enabled
- a bit slower startup time but okay
- a bit more RAM usage