Falkon

Recent versions of falkon (3.2.0 and later) have a habit of updating the profile in an incompatible way. If you share /home between several systems on the same machine, this means that you should update update falkon on each of those systems: the first time, the profile will be automatically updated, but after that kill falkon when exiting and do not use falkon on the other systems until it has been updated (and similarly kill it on exiting if not all the systems have been updated).

If you use an older system, the previously updated config is saved in ~/.config/falkon/profiles/default/browsedata-backup.db and falkon starts without any profile information. When all systems on that machine have been updated, you can probably copy that file to browsedata.db.

You may wish to keep a note of the important items before upgrading.

AFAICS, there is no way of specifying a profile for falkon. There are reports that falkon can save sessions (groups of tabs for different purposes), but presumably those use the same profile.