Linux

You are on the right track. Installing Debian packages don't require password to access shared libraries but to write into system wide directories. That way you don't need to install every software separately for every user. Flatpacks are 'self sufficient' packages and thus often way bigger, since they don't generally share resources.

From security point of view there's not much difference in every day use for average user. Sandboxed flatpacks can be more secure in a sense that if you harden your system properly they have limited access to the underlying system, but they can be equally unsafe if you just pull random software from a shady website and run it without any precautions.

Flatpacks tend to have more recent versions of the software as they can 'skip' the official build chain and they don't need to worry about system wide libraries. Tradeoff is that the installations are bigger and as flatpacks run on their own little sandbox you may need to tinker with flatpack environment to get access to files or devices. Also if you install flatpacks only for your user and you have multi-user setup other users of the machine can't access your software, which might be exactly what you want, depends on your use case.

Personally I stick with good old Debian packaging whenever possible, I don't see benefits of containers like flatpack on my own workstation. Newer software releases or using software not included in official repository are pretty much the only exceptions when flatpacks make more sense to me.

But there's a ton of nuances on this, so someone might disagree with me and have perfectly valid resons to do so, but for me, on my personal computer, flatpacks just don't offer much.