This is something I've read in passing, but never encountered an explanation of why. For example, Wikipedia says:
Another common place one can see dipoles is as antennas for the FM band; these are folded dipoles. The tips of the antenna are folded back until they almost meet at the feedpoint, such that the antenna comprises one entire wavelength. This arrangement has a greater bandwidth than a standard half-wave dipole.
Wikipedia isn't the only one with this notion: see comments to this answer:
it was my understanding that a folded dipole is still full length, just doubled over to increase bandwidth. Am I incorrect?
antenna-theory.com, which I'd consider at least three times more reliable than Wikipedia, doesn't say anything about bandwidth, but does say this:
Because the characteristic impedance of twin-lead transmission lines are roughly 300 Ohms, the folded dipole is often used when connecting to this type of line, for optimal power transfer. Hence, the half-wavelength folded dipole antenna is often used when larger antenna impedances (>100 Ohms) are needed.
I could then see how, if you had to use 300Ω transmission line, you might get better bandwidth with a folded dipole as you wouldn't need a matching network, which might limit bandwidth or incur additional loss, but that's a long guess.
So, really why do folded dipoles have greater bandwidth? Or is that just an unsubstantiated rumor?