This has been requested on Thunderbird since the year dot, but the recent release of Thunderbird for Mobile has created a clear discrepancy between mobile and desktop versions. On Tbird for Mobile you can choose the reply header format under Settings / [account] / Sending mail / Reply quoting style. The choices are "Prefix (like Gmail)" and "Header (like Outlook)".
I've used the various reply header plugins since around version 3 of Thunderbird, but if Mozilla are looking to grow the user base, especially into corporate use (as the development of Exchange capability suggests, and is well under way), it really is about time someone sat up and took notice that they are persisting with an omission which could drive new users back away again.
The purist arguments about not needing these details are irrelevant. Some won't want it, and it's not going to be forced on you. But for corporate environments with never-ending email chains where emails are often curtailed or selectively replied to, the use of a full reply header is vital, and provides audit capability where needed. It's also not hard - the code is already there as it's used for a Forward.