IMO 1/2 inch is the best everyday rigging line. I like stable-braid the best for cost/wear.
I hae a 9/16 for my big line and have acess to 3/4 for very big stuff.
Usuall, when you get into very big wood, you do not want very dynamic rope, but that is one of the factors in tensil. The 3/4 I use is a tighter weave, cuasing less streach, so we can block bigger chunks lower.
Only that and speed-lines are where I like low streach cordage. My 1/2 inch is high streach adding some extra SWL for running log sized chunks and big tops out with The Winch.
I like a 200 ft 1/2 inch, 150 of 9/16 and 100-120 of 3/4 because we do not need to haul that real heavy stuff all that high up. I only need 3/4 a few times a year.