Which factory reset should I use? I have the motorola droid 3 and it can be factory reset from either the settings menu or the recovery menu. What is the difference between the two?
Results should be the same, so you can use either.

The item in the recovery menu you could count as a "backup switch": How else could you reset a device which refuses to completely boot up? That would otherwise be a "vicious circle": In order to boot up you'd neet to factory-reset – but in order to factory-reset, you'd need to boot up. So with the recovery menu, you've got a "reserve switch" for cases like that.

The switch in settings, on the other hand, is easier to find for "novice users" not aware of those "Vulcan nerve pinches" (or "three finger salutes", whatever you prefer) to boot the device into "special modes".