Flatpak is a system for building, distributing and running sandboxed desktop applications on Linux.
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Pros
Pro Cross-distribution
You can install flatpak packages on any distro you want.
Pro fast
searching, installing and updating are faster than others in my experience
Pro Doesn't bog system down like snaps.
Plus it's not proprietary.
Pro Application sandboxing
All applications are limited to a set of predefined permissions, enhancing privacy and security.
Pro A well-written documentation
Pro Flexible runtime management
You can install a lot of runtimes for different apps, making applications a lot more compatible while still allowing some applications to share their runtimes.
Cons
Con Bloated
Due to the way Flatpack handles packaging, this can lead to a large cache being created which quickly inflates to unreasonable sizes. Not only this, but using flatpack requires a large chunk of space to be reserved for it's own file hierarchy.
Con Difficult to export packages
It is difficult and convoluted to export installed packages and move to another system.
Con Doesn't work well with CLI programs
Invoking CLI programs can be a pain. From the weird reverse DNS package names to difficulty in easily managing container environment.