FM altimeters are industry standard for aviation, and measure the time delay by comparing the phase shift in the reflected signal - which makes them very accurate. Pulse altimeters must use a deramping chirp to mix with the reflected chirp to measure the shift, and the measured frequency shift is thus only an estimation, giving lower accuracy (3.125 nanosecond chirp gives a resolution of about half a meter).
Frequency modulated radar altimeters have a height limit of about 5000 feet. Pulse altimeters are used for higher altitude applications (mostly satellites).