Nick1, please don’t confuse FLS and GLS, they are two entirely different systems.
FLS uses the FMS to calculate a pseudo LOC and GS beam and effectively uses the same indications as when flying an ILS approach albeit with a “double diamond”.
When flying a GLS approach the MMR uses the local GBAS system / channel.
FLS is entirely FMS generated whereas the GLS still uses GBAS which is an external system.
Both are highly accurate although a three degree FLS beam in very hot conditions might end up being misleading, GLS doesn’t have this issue.
Have flown both approaches and done autolands of GLS approaches which with an FLS approach equally is not possible.