I own and have carried in both, and I prefer kydex. I made a quick list below of what comes to mind with regards to the good and bad of both, but it's hardly extensive.
Leather Pros and Cons:
+ Looks better then kydex when worn with a suit
+ Slightly more comfortable when worn IWB
- Generally thicker then kydex holsters
- If you want a non-production holster lead time is usually more then half a year
- Maybe this has changed since I last shopped for a holster, but leather tends to be more expensive then an equivalent kydex offering
- In my experience, leather is harder on a gun's finish
- Leather will break down from exposure to the elements much quicker then kydex
Kydex Pros and Cons:
+ Thinner then leather
+ Lighter then leather
+ Many are modular or have user switchable attachment points (like raven concealment's line of holsters)
+ Usually cheaper then leather and has shorter wait period for non-production offerings
+ More durable then leather
+ Allows for a faster and more consistent draw
+ Doesn't collapse when the pistol is drawn
- Doesn't look as nice as leather
- Many don't find the texture of kydex to be particularly comfortable