Guy on mud will often make things a lot more complicated than they really are. That said, there is no simple single answer to your question. !0,000 lbs ain't that much pull. Lots of us have snapped 20K straps. Plenty of people have failed to extract with a 10K winch pulling. There are all sorts of mud, and a whole bunch of other factors affecting how hard the rig will be to pull out. Mpt to mention what sort of approach you take to it, what sort of recovery rig and equipment you are using and the skill and experience of those involved.
FWIW, I'd go heaver than 10K anything for any sort of stuck that is worth any real attention.
Mark...