- Cross-distro packaging (no need to provide N package formats - this one runs on all distros)
- Faster update cycle for each app, if the package is maintained by the original developers
- Sandboxing
- Better compatibility all around, as the package runs the same on all distros (as opposed to some too-old or too-new module breaking something on X distro)
- Some other goodies, like checking new releases of the source on Github etc
Flatpak's drawbacks:
- Modules are not shared, which can result in somewhat larger packages and potential vulnerabilities
- Many packages are community-maintained by people who are not necessarily experts in the Linux ecosystem. Distro-provided packages usually have tighter requirements
Personally, I use Flatpaks for the sandbox. I restrict all apps very heavily.