The whole idea of maintaining module systems in a perfect sync on several systems as compared to i.e. just rsync-ing SIFs sounds strange to me. Often HPC systems (or rather their admins) are fairly (and for a good reason) conservative, keeping old system and libraries versions. Your mileage may vary, but in a small benchmark of a bioinformatics program called samtools depending on the version the fastest binaries were either run in a conda environment or inside singularity container using Clear Linux distro. Binaries compiled using either system's GCC or from a module were slower.

One would have to repeat it throwing in at least Spack to see if this still holds water.