Feed-point impedance is a big difference, which can make the folded dipole easier to work with in some designs (such as for the driven element in Yagi or Log-Periodic directional antennas).
Assuming resonant antennas in each case, as in half-wave folded-dipoles and full-wave loops, the input impedance of a full wavelength loop is about 100 Ohms, where a folded dipole is about 300 Ohms (a regular dipole is about 73 Ohms, or roughly 75 Ohms for simple math).
Other differences, such as polarization, required antenna area, ease of construction, and bandwidth also exist. Are you considering one or the other for a specific application?
Matt
