Orbital neutron spectroscopy has become a standard technique for measuring planetary surface compositions from orbit. While this technique has led to important discoveries, such as the deposits of hydrogen at the Moon and Mars, a limitation is its poor spatial resolution. For omni-directional neutron sensors, spatial resolutions are 1-1.5 times the spacecraft's altitude above the planetary surface (or 40-600 km for typical orbital altitudes). Neutron sensors with enhanced spatial resolution have been proposed, and one with a collimated field of view is scheduled to fly on a mission to measure lunar polar hydrogen. No quantitative studies or analyses have been published that evaluate in detail the detection and sensitivity limits of spatially resolved neutron measurements. Here, we describe two complementary techniques for evaluating the hydrogen sensitivity of spatially resolved neutron sensors: an analytic, closed-form expression that has been validated with Lunar Prospector neutron data, and a three-dimensional modeling technique. The analytic technique, called the Spatially resolved Neutron Analytic Sensitivity Approximation (SNASA), provides a straightforward method to evaluate spatially resolved neutron data from existing instruments as well as to plan for future mission scenarios. We conclude that the existing detector--the Lunar Exploration Neutron Detector (LEND)--scheduled to launch on the Lunar Reconnaissance Orbiter will have hydrogen sensitivities that are over an order of magnitude poorer than previously estimated. We further conclude that a sensor with a geometric factor of approximately 100 cm(2) Sr (compared to the LEND geometric factor of approximately 10.9 cm(2) Sr) could make substantially improved measurements of the lunar polar hydrogen spatial distribution.