I am a user of Firefox 26 from the beta channel. (OS is Win7-64 Home Premium.)
Today I downloaded and installed Internet Explorer 11 onto a laptop. It required a restart of the laptop, which spent a long time "adjusting settings" before it eventually shut down and restarted.
After restart, everything seemed fine until I started up Firefox, which crashed immediately it was started, before even getting up any browser window. This was consistently repeatable and popped up an error window with the choice of restart or resetting all the Firefox settings - the latter I wished to avoid doing.
Otherwise, Firefox worked OK in protected mode.
So, as an experiment, I download Firefox 26 from the beta channel and installed it. Worked a treat.
UPDATE 2013-12-25 1142hrs: - just for the record in this thread I started:
The fact of Firefox crashing after I had installed IE11 was, it seems, just a coincidence. I kept FF on its last stable ß update and stopped allowing FF to automatically update. After skipping 3 updates this way, I allowed the 4th one, and it was stable. Subsequent updates have been stable also.
Meanwhile IE11 has been running solid/stable all the time.