I have very good relative pitch and used to moonlight as a harpsichord tuner. I can tell you if an instrument is in equal temperament - an equal-tempered fifth and an equal-tempered third all have very distinctive sounds. With enough time, I can also identify most of the common baroque temperaments: Just Intonation and quarter-comma meantone stick out like a sore thumb, but tunings like Werckmeister and the others that attempt to be close to equally tempered are harder to pick out by ear since you really need to hear the whole circle of fifths to identify which one is used. However, this skill isn't due to hearing a precise gap between the two notes, but listening to the beating of the overtones of the notes.

Also, professional string players can often tune equal tempered fifths (~2 cents flat of a pure fifth) precisely on their instruments.