IIRC GPS LPV is at best considered comparable to ILS Cat1, and GPS altitude data is pretty much forbidden to be used for that (radio altimeter is required for any kind of low-visibility approach, iirc, plus it's required for TAWS).

In good conditions the approaches might be indistinguishable, especially given that GPS approach once on final will be usually a copy of GPS one, but the safety of GPS LPV is considered much lower, for a good reason.