Granted, Tor tries to upstream as much as it reasonably can to FF, but there's still large differences in defaults that could give away (some bits of) your identity.
It's all baby steps. I don't expect to be fully anonymous this way, just like I know my current setup does not foil more sophisticated tracking.
This is my every-six-months wish/rant on this subject ...
What we need is the ability to 'jail' a GUI browser process.
It is too resource intensive to spin up an actual virtual machine to run a browser window/tab. However, a facility like 'jail' (or zones or, perhaps even Docker) that simply chroots a new process with its own network interface, etc., does not have any of that expense.
It really is just a fancy chroot and the expense is limited to the overhead of just the process you're running.
If you could 'jail' a GUI application, you could have a browser window that was not merely its own cookie domain or history domain, but that was on an entirely different network and it's own chroot.