Granted, if the sort of comparison you're after is of the 'my tractor will pull more than your tractor' variety, then the all the factors you mention, and many more, will have an impact on who wins. I guess my understanding of the OP's comment seemed to presume something more akin to a standardized testing scenario, where factors like fuel temp, pulling speed (from rest), tire design, etc., would be consistent among the test candidates.
I assume by 'peak and constant' HP in this context, they also perform a sort of endurance test, in other words, loaded pull over distance vs. a maximum pull effort. That also seems like a different sort of testing scenario than what was implied by the OP.