We report strict upper limits to the radio luminosities of three neutron star low-mass X-ray binaries obtained with the Very Large Array while they were in hard X-ray states as observed with the Rossi X-ray Timing Explorer: 1E 1724-307, 4U 1812-12, and SLX 1735-269. We compare these upper limits to the radio luminosities of several black hole binaries in very similar hard states, and find that the neutron star systems are as faint as or fainter than all of the black hole candidates. The differences in luminosities can partly be attributed to the lower masses of the neutron star systems, which on theoretical and observational grounds are expected to decrease the radio luminosities as M^0.8. However, there still remains a factor of 30 scatter in the radio luminosities of black hole and neutron star X-ray binaries, particularly at X-ray luminosities of a few percent Eddington. We find no obvious differences in the X-ray timing and spectral properties that can be correlated with the radio luminosity. We discuss the implications of these results on current models for the relationship between accretion and jets.

9 pages, 5 figures, two of which are color. Submitted to ApJ