Pros:  Leather makes a very strong and durable leash, that if properly cared for can last a lifetime.  Leather is also comfortable on your hands and does not burn your hands like nylon can with fast tracking dogs.  

Cons:  Leather usually needs to be broken in with time and use.  Leather also needs to be dried when saturated with water.  As fine leather boots need care, leather leashes also may occasionally need oiled or lotioned to keep them from cracking or wearing too quickly. 

Each leash is recommended due to its quality craftsmanship and strength.  These leads have brass hardware, metal rivets (rather than just thread), proper braiding and quality materials.  You can find cheaper leashes but when your life or liability is at the end of that line, you want the best!

"My primary 6' leash is leather and I've used it almost every day for years with my police K-9.  For detection work, leather seems to be the most tactile and comfortable material for allowing the lead to glide through your hand as you allow your dog to search.  I also keep a leather 8" tab on my duty belt as an emergency backup leash which I highly recommend.  On one particular barricaded suspect call, that 8" tab quite literally may have saved me."  -Matt Cox, Impact Dogs owner