A new mission called GRACE Follow-On is now flying to continue the measurements started by the GRACE mission, and to test a laser interferometry system for making more accurate measurements of the satellite separation. In this paper we discuss the potential scientific benefit of strongly reducing the acceleration noise in a Next Generation Gravity Mission (NGGM), compared with that for GRACE and for GRACE Follow-On. A useful way of comparing the scientific benefits is from the view point of how well they can be used to test different procedures for estimating the changes in the geopotential based on sources of geophysical information other than satellite gravity results. In particular, changes in hydrology, the atmospheric density, and ocean conditions can make large and very non-uniform changes in the geopotential in short periods of time. To make the discussion as simple as possible, we consider mainly the variations in the geopotential at altitude along the satellite orbit for different ground tracks. For the NGGM, we initially assume laser interferometry between the two satellites but the same satellite acceleration noise level as for the GRACE-Follow-On mission. Then the total measurement noise level at long and medium wavelengths would be only moderately below the geopotential variation estimation uncertainty. However, if the acceleration noise level were sharply reduced by replacing the GRACE-type accelerometers by simplified gravitational reference sensors, it appears that considerably improved tests of different procedures for geophysical estimates of the geopotential variations could be made.