After trying many different types of fabric as outside pockets, my favorite is now a durable nylon fabric, but only with a bulge type of construction (opposed to pleats) and split up into smaller pockets rather than one big pocket.
Pros: Drains very well. Some can be stretchy. Can see things in the pocket. Lightweight.
Cons: Certain kinds don't stretch much. Not too durable, unless you use heavier, beefier mesh.
Experience: I love being able to see things in the pockets and having water easily drain from the pockets, but I find durability to be an issue.
Pros: Drains well. Very stretchy. Can kind of see things in the pocket. Pretty durable.
Cons: Heavy. Not quite as durable as Dyneema X types of fabric. Not the easiest to work with.
Experience: Despite the weight, I prefer Lycra over lightweight Mesh for the extra stretchiness and durability.
Dyneema X type of fabric
Pros: Very durable. Easy to work with. Fairly lightweight.
Cons: Doesn't drain well. Doesn't stretch much. Can't see things in the pocket.
Experience: This has been my favorite pocket material, because I like having my pockets very durable. However, I only like them as pockets when they are constructed large enough to compensate for the lack of stretch, and when they are split up into multiple pockets instead of one big pocket, because it's much harder to find things in one big pocket that you can't see through.
Bulge Construction - This is where you cut squares out of the two bottom corners of the pocket and then sew the cut together. Similar to a lot water bottle pockets.
Pros: More volume for non-stretchy fabrics.
Cons: If the pocket is close to the bottom of the pack, it can allow the pocket fabric to come into contact with the ground more often.
Experience: I prefer this with nylon fabrics as pockets for the extra volume. When constructing, be sure to measure out the pocket big enough to compensate for the cut squares.
Pleat Construction - This is where you fold the bottom of the fabric upon itself and stitch it in place.
Pros: Keeps the pocket off the ground more than the bulge. I think it looks nice with mesh.
Cons: Less volume at the bottom of the pocket.
Experience: I would only use this type of pocket construction for very stretchy materials like Lycra. Otherwise, I find myself wanting more volume at the bottom of the pocket.
Well, that is my take on it. I may have left out a few pros and cons with some things that others may think of, but hopefully this will help you some.
Edit: I forgot to add that you can use different fabrics for different parts of the pockets if you desire more stretchiness, durability, drainage, etc. in certain areas. And you can always use grommets or some type of drainage hole for non-draining fabrics.