I never heard of snap or flatpack before you began advertising them with LinuxQuestions threads. So I looked up explanations of snap and flatpack. My answer to your question is that I think it would be counterproductive to mix three different package managers on my system. So I won't.

I will only use a single package manager on my system. At various times I have used rpm or debian. Both rpm and debian are far superior to snap and flatpack so I cannot see snap or flatpack ever being used on a system as the exclusive package manager.

Just got used to the way things are.

So no. Don't run either. But then. My Gnu/Linux needs are simple.

Some folks I know who run what I run use em though to get past the systemd limitiations our distro uses since packages are enclosed.

I always opt for the repo package (Debian Stable) if it does the job for me. I use FP & AI to help out with any v. outdated repo software (as can be the case with Debian).

I use .deb and Flatpak. I find Snap to be slow to start and questionable as a viable option as of now. The biggest short coming of Linux is compatibility with devices like GPS, Radar detectors, and so on that require updates through a USB connection. There is absolutely no Linux alternative software of any kind for these devices.

In Fedora I just use the official repositories. If a package is not available there, then I search for rpms elsewhere, download them and install them with dnf package manager. If I don't find rpms then I search for binary files (those *.tar.gz) and copy them to ~/opt so that they can be automatically updated without starting them with admin rights in future.
I use snap only as a last resort.

I use Flatpak as needed preferring repositories wherever possible. Some things though. I try to avoid installing random .debs as I have no idea what they may try to replace from the systems expected files / libs. Don't much care for PPA's either when I'm on any *buntu variant. I limit my flatpaks to simplenote, zoom, albion online, and makemkv. From this perspective I get the best of both worlds.

I don't use any snaps that aren't directly provided via the Ubuntu package manager though. I don't oppose it, just a choice.

If you are a source kinda guy (I am) then either one is a bit offensive.
The entire purpose of both is to hide things form the user. While the goal, run on any Linux install no matter what packages are installed, seems productive you only get that with a larger load, performance issues, and hidden detail. If I need something my distribution does not provide as a native application, I would rather pull and examine the source, then compile it myself.

I prefer native package managers like .deb (apt) and .rpm (dnf) ... But now with (K)Ubuntu going to snap for Firefox... I use snap for that app. Seems to work fine. I also use appImage for FreeCad so I can be using the latest.