  It is now clear that a subset of supernovae display evidence for jets and are
observed as gamma-ray bursts. The angular momentum distribution of massive
stellar endpoints provides a rare means of constraining the nature of the
central engine in core-collapse explosions. Unlike supermassive black holes,
the spin of stellar-mass black holes in X-ray binary systems is little affected
by accretion, and accurately reflects the spin set at birth. A modest number of
stellar-mass black hole angular momenta have now been measured using two
independent X-ray spectroscopic techniques. In contrast, rotation-powered
pulsars spin-down over time, via magnetic braking, but a modest number of natal
spin periods have now been estimated. For both canonical and extreme neutron
star parameters, statistical tests strongly suggest that the angular momentum
distributions of black holes and neutron stars are markedly different. Within
the context of prevalent models for core-collapse supernovae, the angular
momentum distributions are consistent with black holes typically being produced
in GRB-like supernovae with jets, and with neutron stars typically being
produced in supernovae with too little angular momentum to produce jets via
magnetohydrodynamic processes. It is possible that neutron stars are imbued
with high spin initially, and rapidly spun-down shortly after the supernova
event, but the available mechanisms may be inconsistent with some observed
pulsar properties.
