What would be the implications if these two were found to not be equivalent? In terms a biologist could understand, please. ;)
If one wants to try to unify all fundamental interactions, we actually predict deviations from the equivalence principle (at a super-duper-tiny level). But we know that general relativity is not the end of the story, as gravity cannot get quantized (in contrast to the three other interactions). So deviations must happen at some point. Observing them would hence pave the way to understand better the unification of all fundamental interactions.
Also, in my field, I usually deal with measurments on the order of +/- 10% error and custom equipment that is made to more than 1 mm tolerance is considered super precision machined. (Bioreactors, not talking about the super expensive lab equipment) The idea of dealing with 14 digits of precision is mind boggling. Like, my pH probe loses a hundredth point if my lab gloves are extra static-y that day.
Gravitational wave measurements are even more amazing in terms of precision! :D