We report precise measurements of differential x-ray scattering cross sections in Ne and He from 11{endash}22thinspthinspkeV and develop a method for obtaining predictions of comparable accuracy (1{percent} ). The measurement of ratios (total scattering in Ne to He and Compton to Rayleigh scattering in Ne) facilitates comparison to theories. We find evidence for the need to include nonlocal exchange, electron correlation, and dynamic effects for an accurate description at low Z and conclude that no single current theory is sufficient. {copyright} {ital 1998} {ital The American Physical Society }