Specifics of Private space:
exists only in Owner profile
doesn't have access to phone and sms (fin apps may fail if they depend on it)
shares clipboard with "outside" (devs are considering to implement a setting for that), though it may be useful if you need to copy-paste single-use CC number from Revolut, for example
Specifics of non-owner user profiles:
can't install tools like Termux
can't configure some of system-wide settings like private DNS (can do it for apps that allow it, like Vanadium etc)
can't enable hotspot (only owner can)
(UPD) can't disable/enable internet, it's only wifi and airplane mode that can be turned on/off
can't enable internet tethering (usb/eth/bt)
can't start desktop mode, unless it was started in Owner, so have to switch to owner and then back. Others have reported it works for them without the switch
Specific of switching between profiles:
if to use separate user profile, media will stop if once switch to fin-profile
only 3 profiles can be active at the same time (apps not frozen)
tethering that was enabled in Owner profile gets disabled once one switches to another profile
(UPD) connected Bluetooth devices get disconnected (in my case they don't reliably reconnect) so you can't listen to music or be at a call while switching