The biggest difference between kids who never play club vs. those that do, is generally speaking, the kids that have never played club (and are decent players), never reached a level in town where they can't skate around the other team.
This creates a massive problem for them when they get older and transition into late middle-school and into High School, the ice gets smaller, and creating time and space becomes more difficult.
They can't make that transition because they've never had to.
Club hockey when appropriately placed, teaches your player how to create time and space, essentially the most important piece of playing hockey.
Now, add to that the potential of more ice and better run practices, you can see why the spread grows between a player playing it vs. not playing it.
I will say there are many clubs around that are no better than town by way of overall talent. But at the end of the day if you add a good practice to a kid who loves it, they'll develop.