Security. Use apt

One thing that hasn't been mentioned yet is interopability, that is, flatpak interacting with the rest of your system.

I'm not that familair with flatpak, but in my brief experience with the steam flatpak, I had trouble getting it to recognize my controllers. Steam installed through pacman (Arch's package manager) had no such issues, on the other hand. My hunch is that this has to with flatpaks being more isolated from the rest of your system.

Im pretty sure that's just some kind of permission issue, but it can be nice to not have to troubleshoot acces rights and the like. But this is obviously a double edged sword: more isolation may also mean more security, just at the cost of ease of interaction with other components.

apt is good for most things.

Flatpak is good for applications where you want the people who write the software to be creating the releases and for closed source apps that you want to isolate a bit from your system.

For example, on a new system you might install everything using apt except for Zoom. Zoom isn't in the Debian repos, it's closed source and proprietary. But you can get the official Zoom application using flathub. Zoom will also be fairly isolated from the rest of your system so it has less access to your files and can be removed more cleanly later on if needed.

In addition to other people's comments, flatpaks are usually more up to date than their apt counterpart (expecially those from the debian stable repositories).
I run debian and I deliberately installed some software from flatpak (eg. Ardour and Guitarix) because the deb package is a whole version behind.

I'm not very knowledgeable about this sorta thing. I'm just gonna say that modding games with the Flatpak version of Steam is way easier.