Naturally, I would prefer leather...:o)
With the treatments they have today, such as Sno-Seal etc, it is not hard to weatherproof the leather if you prefer it.
Personally, I use Neatsfoot Oil as the first application, then a light coatin of Mink Oil. Heavier coats of Mink Oil tend to darken the leather a bit more but if you work it into the stitching and the leather, it will totally waterproof the sheath.