My understanding is that Pop uses Flatpak sparingly, whereas Canonical is pushing Snaps for an increasing amount of software.
That is, IIRC, you get (say) Firefox via Debs in Pop. Canonical wants to install it via Snap.
IMO Flatpak is a great option for a set of desktop software where packaging across distros may be problematic for some reason. I use the Firefox Flatpak on Fedora / RHEL because it doesn't disable the video codecs, for instance. The native package doesn't have some codecs enabled.
Canonical is (AIUI) pushing Snap for desktop and server software. And Canonical is the only source of Snaps, I believe? With Flatpak you get Flathub but AFAIK anybody could set up a repo of Flatpaks.
Flatpaks have some startup time penalty, but it's an order of magnitude better than Snaps. They also have way better disk usage characteristics per installed package than Snaps do (they scale better).
You can use them side-by-side on the same system. Install a dozen of each and take some measurements.