My B+W regular filters are about 5mm from the front edge of the metal to the threads.
The main point of the slim filters is to reduce vignetting with wide angle lenses. Otherwise the difference is immaterial unless you're concerned about eliminating weight a gram at a time or your lens being too long by 2mm.
Forgot one other thing that might be important. The slim filters (IIRC) don't have a front thread for stacking multiple filters. The regular filters do. Not important for the way I work, but could be for some.
As a point of interest, B+W makes some extra wide filters, where the fit to the lens in one example is a regular 55m thread, but the front filter thread goes to 72mm, again to prevent vignetting.
According to the people at The Filter Connection (no affiliation, customer only), the B+W "F Pro" filter series is 4mm thick, compared with 3mm for the slim variety. They will say "F Pro" on the ring. Apparently previous standard B+W filters were 5 mm thick.
This has been on my mind as well, since I'm trying to outfit a couple of new lenses with UV filters and polarizers. No brainer for the telephotos, but I wonder whether it would matter for the wide-angle zooms at their short end.
I'll soon find out as the filters are en route....