What effect does pulley diameter have on efficiency?
A larger diameter pulley wheel (aka sheave) is slightly more efficient than a smaller diameter pulley. But, a larger pulley has increased bulk, weight more and cost. For example, in a 1:1 haul, you gain about 7% efficiency going from a 1.5” pulley to a 3.75” pulley. This efficiency increases with really big loads (600 lbs+) and larger mechanical advantage, such as 6:1 and 9:1. So, it's probably of interest to mountain rescue teams, of moderate interest to big wall climbers, and not very relevant to alpine climbers. As long as you use a good quality pulley, the diameter doesn't matter much.
In the real world, on, say, a crevasse rescue, you're probably not going to notice the difference between a pulley that's 80% efficient versus a pulley that's 90% efficient. Get a 1.5 inch rescue pulley from a name brand company and don’t stress about the actual efficiency rating.
But note the low carabiner efficiency - about 53%, ouch!
Is it better to use static rope or dynamic rope in a hauling system?
Steel cable has essentially zero stretch, and offers the highest efficiency. Next best is static rope. Third-best is dynamic rope. Alpine climbers may only have a dynamic rope available, so they may not have a choice. (However, this is one more argument in favor of using a static rope for glacier travel, see this tip for more on that.) Big wall climbers, however have a choice between a static or dynamic haul rope. Static haul ropes are more popular on big walls, and this is one of the reasons, greater hauling efficiency.
When you haul a big load with a dynamic rope, you have to pull all the “stretch” out of the rope before the load even starts to budge. As you might imagine, this is not much fun. Once all the “stretch” has been removed from the rope, if you then pull in a steady constant speed, all ropes are going to behave pretty much the same way. However, in the real world, you're going to have a pull that isn’t so smooth; you're going to accelerate and decelerate. When you do this, the dynamic rope is stretching and relaxing, back-and-forth, and this absorbs energy and lowers your efficiency.
See the graph below. Steel cable, with a large diameter pulley, is about as good as it gets, 98% efficiency. The other four flavors of static rope are all pretty darn close. Note again, the efficiency increases slightly when you go to a larger diameter pulley wheel. Too bad they didn’t test dynamic rope in this experiment, but it was done by a mountain rescue team, and they almost always use static ropes for hauling systems.