safety pee:
MLS works fine in rain.
The FAA favoured GPS only after fighting for world leadership of the MLS design with an inferior system, then discovering that the costs of re-equipping was not justified by their requirement for Cat 3. Thus the already funded GPS was selected as being capable of achieving Cat 3 integrity in the future at lower cost.
All I know about FAA MLS in the mid-1970s was the airlines wouldn't touch it. They had just spent a bundle on fail-active autholand tied to high-quality ILSes.
GPS can do great curved paths although I am not sure where those would be required at the major airports that have CAT III, at least in the U.S.