After recent update, Filezilla crashes every time I try to fire it up. Eventually, reinstalling it with Synaptic Package Manager worked out.
I noticed the version available via Muon Discover is 3.7.3. At this time The latest stable linux version of FileZilla Client is 3.14.0

Do we need to skip Muon and add a new PPA for Synaptic to update? Or should we simply follow the link FileZilla offers to download their latest tarball of the full new version?

I would stick with the version offered in the repo as this is a widely tested one.
If you really need the newest version I would suggest searching for a ppa.
Downloading the tarball would mean you need to compile the app itself and install it yourself.