The "leather" sheath for wave is uncomfortable for horizontal carry, too stiff, stick with nylon. Plus it (leather) only fit small width belt.
As with many things it is all subjective to the user, in your opinion it may be too stiff, for others this is a positive. I and some others I know prefer the leather sheath mounted horizontal.
I find the nylon mounted horizontal (yes I have tried it) is too flimsy, and when catching on things tends to pull uncomfortably where the leather either just bounces around snags or just smashes its way through whatever the sang was (tree branch etc).
The leather will fit a reasonably wide belt, no it will not fit on a 2" plus wide equipment belt but does comfortably (after the first few fittings) fit my 1 7/16" belt.
My Leather wave sheath regularly carries a Fenix LOD or similar AAA single cell flashlight in one of the side elastic sleeves and usually a mini sharpie marker or spare AAA cell in the other side.
Anyone in Oz WTS any nylon wave sheaths I have 2 x PALs mount nylon sheaths and about 1/2 doz x standard (new type) nylon sheaths to spare.
I still also have an original "brown leather" old style wave sheath that has after many years of abuse, sports a wonderful pateena that only "old leather" can emulate which looks A1 mounted on a old style wide brown leather belt. (This is my going out sheath).
Just balancing out the pros and cons