  Binary systems comprising at least one neutron star contain strong
gravitational field regions and thereby provide a testing ground for
strong-field gravity. Two types of data can be used to test the law of gravity
in compact binaries: binary pulsar observations, or forthcoming
gravitational-wave observations of inspiralling binaries. We compare the
probing power of these two types of observations within a generic two-parameter
family of tensor-scalar gravitational theories. Our analysis generalizes
previous work (by us) on binary-pulsar tests by using a sample of realistic
equations of state for nuclear matter (instead of a polytrope), and goes beyond
a previous study (by C.M. Will) of gravitational-wave tests by considering more
general tensor-scalar theories than the one-parameter Jordan-Fierz-Brans-Dicke
one. Finite-size effects in tensor-scalar gravity are also discussed.
