I measured both (repeatedly) while setting up my press. I haven't measured again in several thousand rounds.
Flare was set to .384", and has worked well, including with my new Lee Inline Bullet Feeder.
The 6th edition of the "Ammo Encyclopedia" lists the mouth OD as .380" in the military section, and .3799" in the sporting section. However, I adjusted my Lee FCD die until a pulled bullet had a VERY light (almost imperceptible) impression on the Blue Bullets I'm using. That measured at .376", prior to pulling the bullet, and I stopped adjusting it. Even though that's .004" smaller than the specified OD in the book, its worked very well for me.