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Yes and no.Is there actually a difference in the distance that the bar travels, from the top to the bottom of each?
Take a look at this picture (from High Bar and Low Bar Squatting 2.0 - Strengtheory)
The bar position difference stays the same (-> the initial difference of the high-bar vs. low-bar position).
So if you would be able to squat to the same depth low-bar style that you can achieve with high-bar (like the person who created that picture assumed) the ROM would be the same.
The thing is you just can't go a#@-to-grass with a low-bar position, because it highly compromises the lower back position.
If you just go to parallel or slightly below parallel (a position that's still achievable with low-bar) the ROM stays the same.
But ROM is a very important factor if you want to determine which uses/works more muscle.
See those two articles A Long Way to Press: Work Capacity, Levers, and Tall People | StrongFirst and The Truth for Tall Lifters | T Nation.
Depending on the individual leverages someone with a 300lbs a#@-to-grass high-bar squat might do more work than someone with a 400lbs low-bar squat to slightly below parallel.