Well, obviously the GAA is what the military uses for "Automotive and Artillery". But this is straight from the Mobile Oil Corp website.
Applications
Mobilgrease 28 is designed for the lubrication of plain and rolling bearings at low to high speeds, and splines, screws, worm gears, and other mechanisms where high friction reduction, low wear, and low lubricant friction losses are required. The recommended operating temperature range is -54ºC to 177ºC (-65ºF to 350ºF) with appropriate relubrication intervals.
Mobilgrease 28 is recommended for use in landing wheel assemblies, control systems and actuators, screw jacks, servo devices, sealed-bearing motors, oscillating bearings, and helicopter rotor bearings on military and civil aircraft. Subject to equipment manufacturer approvals, it can also be used on naval shipboard auxiliary machinery and where superseded specifications MIL-G-81322 (WP), MIL-G-7711A, MIL-G-3545B, and MIL-G-25760A are recommended.
Mobilgrease 28 is also recommended for industrial lubrication, including sealed or repackable ball and roller bearings wherever extreme temperature conditions, high speeds, or water washing resistance are factors. Typical industrial applications include conveyor bearings, small alternator bearings operating at temperatures near 177ºC (350ºF), high-speed miniature ball bearings, and bearing applications where oscillatory motion, and vibration create problems.
Mobilgrease 28 is qualified by the U.S. Military under Specification MIL-PRF-81322, General-Purpose, Aircraft, and Specification DOD-G-24508A (Navy) for shipboard auxiliary machinery. It is a U.S. Military Symbol WTR and NATO Code Number G-395 grease.
The Arresting gear grease has Mobilegrease 28 right on the pail. The Aviation Grease Just has Mil-G-81322D on it...but the Mobilegrease 28 is recommended wherever Mil-G-81322D is used.
So Either one would be good for automotive use, just the aviation grease is a higher temp and waterproof. And the Mobilgrease 28 website says it is a synthetic base also.