I believe Flatpak is safer than the AUR, as there is comparatively more vetting by third parties (e.g. Flathub). Also, the apps you install are sandboxd, which has upsides in terms of security but may have downsides for certain kinds of app, since permissions for full file access, communication with other apps, etc. are restricted by default.

I like the AUR since it's more "native" than the one-size-fits-all Flatpak, but I use both depending on the use case for that app. Sometimes, one version is out of date, in which case I would prefer Tue other.