Do you mean you're given a choice in Firefox or in other apps? I meant being presented with a private/regular mode choice when opening from other apps, like sharing a link or using "open in browser".

Oh I see, I'm talking about where everything is in firefox, though if you mean just on the regular context menu of any link I don't see that for chrome either. In fact it looks like the only way to do it in either browser is what you said: choose in the settings to either have plain tabs or private by default. Now I'm curious how you managed to do it in other browsers.