  We investigate the radio and gamma-ray beaming properties of normal and
millisecond pulsars by selecting two samples from the known populations. The
first, Sample G, contains pulsars which are detectable in blind searches of
gamma-ray data from the Fermi Large Area Telescope. The second, Sample R,
contains pulsars detectable in blind radio searches which have spin-down
luminosities Edot > 10^{34} erg/s. We analyse the fraction of the
gamma-ray-selected Sample G which have detectable radio pulses and the fraction
of the radio-selected Sample R which have detectable gamma-ray pulses. Twenty
of our 35 Sample G pulsars have already observed radio pulses. This rules out
low-altitude polar-cap beaming models if, as is currently believed, gamma-ray
beams are generated in the outer magnetosphere and are very wide. We further
find that, for the highest-Edot pulsars, the radio and gamma-ray beams have
comparable beaming factors, i.e., the beams cover similar regions of the sky as
the star rotates. For lower-Edot gamma-ray emitting pulsars, the radio beams
have about half of the gamma-ray sky coverage. These results suggest that, for
high-Edot young and millisecond pulsars, the radio emission originates in wide
beams from regions high in the pulsar magnetosphere, probably close to the
null-charge surface and to the gamma-ray emitting regions. Furthermore, it
suggests that for these high-Edot pulsars, as in the gamma-ray case, features
in the radio profile represent caustics in the emission beam pattern.
