3/4 inch is standard equipment, but it depends how you lower the loads!
We have 3 3/4 inch green double braid ropes cut to 210' each, we also have 2 3/4" Arborplex bull lines also 210' lengths- We reserve these line when we are either very close to a home, or we have large material to lower.
We use a 9/16" double esterlon for all of our small diameter lowering. The key is always going to be the weight of the items lowered (load) and the technique utilized when lowering.
It is quite easy to overload a sling of any size if you shock load it or "snub it off", I have had brand new slings break if a groundie decides to hold the load without allowing to to run at all. A matter of fact I had to replace an entire set of steps going up to the deck we were protecting because of our groundie not allowing the load to run. cost more than the final payment on the project! Grrr.
If you are expecting to be "snubbing off" many of the loads then go with the biggest slings or loopies you can buy. But, if you are going to allow them to run, then you can get away with anything in the 9/16 to 5/8 range. I like the whoopie slings as they are very easy to tighten around most trees and spars.
On trees larger than 4' diameter, I utilize a logging chain, with a large clevis (45,000 lb), I have a clevis hook on each end, that I hook back into the chain, then I tie a rope around each hook and chain, to prevent them from coming loose. I also use a regular eye sling, in the 1" size for the largest chunks that are lowered.
Of course on the smallest material that we lower I also use a hank of ArborMaster 1/2" line, I like to lower many medium branches myself this way, I employ the Munter hitch and a friction saver to secure these loads while in the tree tops. See Youtube:
http://www.youtube.com/watch?v=9fs2IjE70Uc
that video shows me lowering the material.
This video shows my groundie lowering the top of the tree, again on a Munter hitch, allowing it to run, you can see how close to the homes this is in the end of the shot.
http://www.youtube.com/watch?v=rs_C5M8mtRE
But, in both of these examples the rope was allowed to run, if the material had been held and it had shocked loaded this tree then the entire tree could have broken off of the base as it was almost totally rotten, and had a wonderful cavity at the root flare.
In short, the keys to remember are your WLL, and the technique you are going to be using on any of your lowering tasks.
Be Safe it is dangerous out there-