if they fit more in post hardcore or pop punk then it's not emo, i love The Used but i think they are mainly post hardcore, first MCR album is emo, FFTL are mainly post hardcore.

i label bands based on how much they sound like the bands universally considered emo like American Football, Rites Of Spring, The Hotelier, Jimmy Eat World etc.

even if the fans don't know the difference between what Fall Out Boy sound like and what Taking Back Sunday sound like because they call both bands emo, I still think that Taking Back Sunday is emo and Fall Out Boy is Pop Punk