I haven't used Chrome in a long time, but this is the primary major thing I miss from it (possibly the only thing).

E.g. we have a family computer that my spouse and I use. I have set up separate profiles for us and forced Firefox to ask which profile to use on launch. But this means that if she has the browser open and has stepped away, I can't just open a new window, switch to my profile, and do things under it. I have to fully quit the browser and restart it.

If I remember correctly, with Chrome the profile was essentially tied to the logged in account and it was possible to have multiple windows open to different accounts. With Firefox you need to sign out of a Sync account before logging in to another.