A spacecraft model mounted in the spin-up rig at the top of the 30-foot ADL drop tower. ADL photo

over other methods of 
analyzing fuel-slosh effects

The Harrison Drop Test has several advantages over traditional air-bearing and forced-motion fuel-slosh testing. All of the relevant dimensionless parameters associated with fuel slosh can be very closely matched between the model and full-scale spacecraft. The associated physical parameters include the shape and locations of the propellant tanks, the mass, center-of-mass location and inertias of the vehicle, the Reynolds number of the fluids and the Froude number, which is essentially infinite during the freefall portion of the test. 
The effects of gravity are essentially eliminated due to the high Froude number achieved with a high model spin rate (typically 1500-4000 RPM). Ground-based testing (air bearing and forced motion) operate at lower spin speeds causing excessive Froude number errors.
The center-of-mass motion due to liquid slosh is replicated in the Harrison Drop Test - as opposed to other methods. Comparisons with flight data have shown that this can be an important effect, especially with large amounts of liquid.
The Harrison Drop Test is the only method (analytical or experimental) that can analyze transient (not just steady state) fuel-slosh effects. ADL first discovered one such phenomenon (dubbed the "transition-to-nutation-synchronous slosh mode") which is mostly associated with centerline tanks. The nutation time constants during the transient periods can be an order of magnitude or more shorter than the steady-state values.