Our 7/8" kinetic recovery ropes are made from Samson Super Strong and have an average break strength (ABS) of 24,700 lbs. We recommend a 3-4 times safety factor vehicle weight vs line strength. So a 6,000 lb vehicle has a 4+x safety factor and an 8,000 lb vehicle has a 3+x safety factor.
Our shop DD is a FJC, 33's, armored front rear side and belly, winch, and a bunch of tools and gear. We have snatched the every living fool out of our 7/8" line without a problem. Make sure you have enough diameter not to break the line but not so much that the line won't stretch enough. If someone gave me a 1" I'd use it and not think twice, but if I was buying a line I'd go 7/8".
You might notice that we currently only offer kinetic recovery ropes in 7/8" because we stock that diameter. We stock that diameter because it is our #1 seller by far. I have a 300' spool sitting on the splicing bench with your name on it.