Treamills, yes. It's not super-exact but will get within a tenth or two of a mile as best I can tell when I run outside with my GPS. Ellipticals I can't speak to.
Love my FitBit One. It syncs with my phone and MFP... it's really kept me on track this year!
I know the HR Monitor question was asked in August, but if anyone else is wondering... I own both and to me, they have two different jobs. I will still log my running into the FB interface, to get the calories burned recorded. I don't use my HR monitor to count calories burned, so I don't know how it compares.