Resistance to bend and flex is the big thing.
Funny thing is, most people don't realize that all of the steel alloys have virtually the same elastic modulus, irrespective of alloy or heat treat condition. You can make a coat hanger out of 1020 or 4340 or 300M, and it'll still flex in your hand much the same.
Now if you're talking about actually pulling something apart, then alloy and hardness have everything to do with it. But in the case of traction bars, it's almost always about flexure, so choose any of the alloys - they'll all behave similarly. High priced alloys really won't buy you much, if anything. Save your money for go-faster parts.