Brands schmands indeed. It's a very good analogy, but missing one vital variable.
I know there are bow technologies and I'm sure there arrow and shaft technologies that make a difference. In archery though, you can't change the way the air plays. In bowling, the lanes can be changed in minutes. Look at some of the day 1 - day 2 score disparities since pretty much forever. Lanes change everything. While winning is more than matching up, the placement of friction on the lanes is the most significant parameter that sets up the field for who does it easy, who does it tough, who scores, who wins and who loses. The favoured players then work out who gets to the top.
As an obvious example, Wall the lanes up (most houses these days) and we significantly reduce the requirement for accuracy and even repetition of release. House shots also hand out a bunch of friction to create ball roll. Wrist guards dispense with a significant component of physical strength and control. Ball cover stocks create massive amplification of a bowler's ability to rotate the ball and generate their own friction. Core engineering makes an embarrassing release come good by flipping the ball track off the thumb hole to allow the cover to get done what the bowler is incapable of. And the balls just get bigger and bigger.
While ever bowling remains a competition to see who can throw the biggest hooking balls of all time straight in order to gain the greatest advantage from the factory engineers, the skills utilised in creating your own ball roll are not only compromised, they are actively discouraged.
Regardless of the brand.