I've been kind of a "sheath guy" for a long time now. I have both leather and kydex options for most of my knives, all of my knives are users.
Leather:
Classic and traditional.
Quiet.
Tends to be more forgiving to the knife blade finish and edge.
Visually appealing, some are true works of art!
I love the smell and feel of fine leather, most people feel the same way.
I promise you will get far more compliments on your fine leather sheath than you ever will with kydex.
Many of my leather sheaths give me a real "pride of ownership" feeling. I enjoy talking about them and showing them off.
Expensive for quality work.
Need regular maintenance; cleaning, oiling and sometimes even stitching.
Getting the sheath wet, depending on your situation, can range from just annoying to being a major problem.
Rots, but if good quality and properly cared for can outlast it's owner.
Can shrink or crack, depending on conditions, if not cared for.
Wear and tear can add up pretty quick even if well cared for. Sometimes I find wear enhances the look, however.
Kydex:(lets assume its well made,crappy kydex work is a major bummer)
Durable, rugged and reliable. Can crack wide open if impacted hard enough, however.
Supports multiple carry options, kydex can be carried in pretty much any position you can dream up.
Excellent retention with out the need of a strap.
Cheap and easy to get.
Super easy to maintain, just rinse em out!
In general, I find them faster on the draw but this isn't always the case.
Easy to add or remove sheath "options" like fire steel loops, piggybacked sheaths, deco flames etc.
Numerous color/camo options.
Not pretty to look at but often have an appealing "modern" and "tacticool" look.
Noisy. Loud on the draw and having branches and twigs clicking and snapping on it while stalking is bad.
Can cause quite a bit of wear to your knife finish and edge. Edge-wear in the sheath is one of my pet-peeves.
I find that the harsh desert sun in my area is pretty hard on them (but it's hard on everything!)
Very few kydex benders can achieve a truly perfect fit. Okuden is my favorite, Buy Brown and Mashed Cat are fantastic.
As a side note I have really been enjoying the nylon from Spec Ops lately (as long as the knife has a good fit). They are durable, affordable, resistant to weather and moisture, molle compatible, quiet, easy to clean, cause minimal edge-wear, offer great retention and not too bad to look at. They have a pocket but I'm not a huge fan of the velcro closure, wish I could find one with a buckle. A bit bulky but not that big of a deal. Two sizes and multiple color/camo options. Never been a huge fan of nylon sheaths but these are really nice.