As someone with a leash trained cat, here's my
Cats can become very comfortable with a harness if it's introduced early and slowly. In other words, don't just wrestle the cat into the harness, clip on a leash and expect the cat to be leash trained.
It is very difficult to get a cat to actually walk with you on a leash (as opposed to wandering wherever they feel like).
Strange surroundings/noises will almost always make even a cat who is very used to his harness nervous and want to fight the leash. If you are taking the cat somewhere new a carrier is best for everyone's peace of mind (your's and the cat's)
WARNING: cats on a leash should never be left unwatched. Due to their love of climbing, unlike dogs they are prone to getting up high, jumping off, and then strangling themselves when their leash doesn't reach the ground.
You do not necessarily need to be holding the leash (Mom hooks our cat to a bolt in the wall so she can garden/water and he can watch, dig, and drink puddles)
but you do need to watch the cat.
What are leashes good for?
-In familiar, safe quiet areas where the cat can wander without being startled by strange noises.
-Giving your cat outside exercize and change of scene in familiar areas
-If you don't mind following the cat around at the cat's pace instead of the human's pace.
-If you are willing to supervise on-leash time