Why a grainy photograph and not a good quality one? I feel you're begging the question here by assuming your conclusion as your premise.

Maybe a better metaphor would be a laser pointed vs a flashlight - assuming they emit the name # of lumens, which one is more useful for exploring a dark room? This is why I think the pursuit of endless precision in calculating the value of irrational/transcendental numbers is an amusing hobby but ultimately a waste of time.