It's dependent on how you want to hold the assembly. Most plate mounted boards I've opened are suspended by the plate. So in this case Alps/cherry PCB height would be different, then you have from the plate surface to the base of the stem, 6.6mm Cherry, 7.1mm Alps. And I have no clue about Alps caps profiles so there's bound to be a height difference there too. So let's ignore how far the switches/caps stick out of the case for now and concentrate on a case that can hold the 2 different assemblies.
If you mount the PCB to the bottom of the case you're going to need standoffs and good locations. Either your layout options restrict the locations, or you restrict layout options (winkey/winkeyless/capslock options/ISO layout/...). Nice area over the numrow, but for a 96 key design, not so much anywhere else except if you can squeeze it in between the main group and the numpad. Then you get to figure out the standoff heights for the 2 (alps/cherry).
If you mount the plate to the case, you've got the variances between plate thickness and heights to figure out and deal with.