Yes, if there is no difference, then we'd likely use the one that is easier or more aesthetic. The heuristic would differ depending on the discipline and the culture of the science.
For instance, Matrix mechanics is equivalent to the Shrodinger wave formulation, but it did not catch on for reasons listed here.
[1] https://en.wikipedia.org/wiki/Matrix_mechanics
Another system that did not catch on, is Nonstandard analysis, which uses infinitesimals. It is equivalent to the standard curriculum analysis that uses limits.
[2] https://en.wikipedia.org/wiki/Nonstandard_analysis
It's hard to pinpoint exactly why these systems weren't chosen. It's not just aesthetics or ease of use. It's a bit of arcane history too. Nonstandard analysis took a while to make rigorous. And by that time, standard analysis had already enveloped the "cult of science." Once standards are set, they rarely change if the current methods are "good enough." I've always sought intuition with everything, so I know about these alternative methods.
I find it sad that so many in academia resign themselves to symbol pushing without a real understanding, and then repeat the same misgivings on their pupils. If methods do exist to achieve better intuition, then we should promote them. Often, alternative yet equivalent formulations do provide that intuition.
HN is a bit of a cult of personality itself but ironically, about every month on the dot, a submission gets front paged - geometric / vector algebra or quaternions, and how they simplify and clarify the intuition behind 3D transformations.
Yet the same HN has curmudgeon gatekeepers that also pop up like clockwork in any science thread, just to make sure all lines of thought correlate to the rote symbol pushing they learned. They didn't gain intuition, so they must feel that it's either impossible to, or that no one else has the right to intuition either.
Anyhow... I hope I answered your inquiry.