What type of competition? The Parnelli Jones Dirt Grip is made for racing and competition on all terrains, especially desert, trail, and rock, but also good in mud and even snow and ice. It's made for racing and also does well at high speeds. It's also known for being good on highway. It's also known for being exceptionally well balanced from the factory.
The only reason I don't use that tire myself is that it's not available in my favorite size (33 X 10.5 R15), but I'm sure it's available in 35" size.
The PJ has the advantage of being made for low and high speed use on all terrains. I don't think the Krawler is made for high speed purposes, though it's obviously great for rockcrawling. The PJ would also be good for rockcrawling since that's among its design goals, but probably the Krawler is better for rockcrawling specifically. However, the PJ is (IMO) the best all around offroad racing tire that's also capable of rockcrawling.
I'll note that the OP didn't mention what type of competition. If he means rockcrawling specifically, then I assume the Krawler would be best, though the PJ would also be good. If he means prerunner racing, the PJ is the best at that, IMO. For all purpose DD use on all terrains, I think the PJ would also be best at that.