Equipment is the easiest way to give someone an edge over a specific foe. Motivation and psychology have a limited role in creating such an edge, especially between two opponents of such similar motivation and psychology.
And of course the Wolves did not possess any advantage in motivation or psychology over other Marines. Nor did they possess greater physical prowess, or greater size. The only remaining ways to improve their odds against Marines would be equipment and training. They weren't given any special equipment and they weren't given any special training. How then can they be more effective as Executioners than another Legion?
Let's analyze the legions.
The word bearers are a bunch of wimps who build churches.
The world eaters tactical book is charge directly at nearest enemy regardless of what happens
Emperors children is more concerned with perfection than getting shit done.
Ultramarines are incapable of thinking out of the box. Frankly by this time the one guy who considered the possibility of astartes vs astartes combat was disgraced.
The dark angels I really don't know the lion probably had his own agenda
Death guard did frontal assaults
Iron warriors and imperial fists worked best against walls
the luna wolves used tip of the spear tactics.
blood angels were CC specialists with have a serious flaw.
Alpha legion avoid direct combat with complicated plans
Night lords use terror
Raven guard use stealth.
salamanders like to burn things
Iron hands appear to use overwhelming force
White scars use fast attack.
The 1K sons are psykers whatever their others tactics are I don't know.
Then finally the wolves, they do the berserker charge of the world eaters and BA but they seem to have more control over it, they also use pack tactics as evident in the night of the wolves.
Aside from the DA and maybe alpha legion the wolves were the only ones who could be executioners, everyone else either didn't specialize in what it would take to kill an astartes. Or wasn't flexible enough to get the job one.