Physicists have devised experiments that can probe the interface between quantum mechanics and general relativity.
If they succeed, the greek phrase "Audaces Fortuna Juvat" will be applicable to these experimentalists (Fortune Favors the Bold).
It's not clear to me that it is actually "Pitting the two experiments against each other". But, experiments that can show gravitational effects and quantum effects simultaneously will be very interesting and important. Some time ago, I read a paper about a proposed experiment to combine gravitational time-dilation and the double slit experiment (in the form of an interferometer). The idea is to have the two paths of the interferometer at different heights. The different rates of time should then impact the phases of each path when they reach the re-combination point. Unfortunately, I have not been able to re-locate the paper.
One of the basic properties of quantum mechanics is that a particle (or quantum system made up of a group of particles) can act as if it is in a superposition of possible outcomes. The most common example is the story of Schrodinger's cat: a cat is sealed in a box; also in the box is a radioactive isotope, a hammer, and a vial of poison; if an atom decays in a certain period of time, the hammer breaks the vial and the cat is killed. So the cat is in a superposition of dead and alive states.
Now, superposition does not really work with something as large as a cat, it decoheres to a classical state too quickly due to interactions of all the particles it is made of, with the environment. That is why they have to use a tiny system in this experiment.
So, in this experiment, the "ball" will be in a superposition of having been struck and not struck by a photon. The scientists are trying to design an experiment that is sensitive enough to measure the curvature of space-time due to the vibrating ball. They want to see if space-time is also in a superposition of curved and not curved by the vibrating (and not vibrating) ball.
What makes this so immensely challenging is that the vibrating quantum system has to be very small so that the superposition can be maintained. And that makes it very, very hard to measure the teeny-tiny effect on space-time. The cool thing about these experiments is they will be directly observing quantum and gravitational effects simultaneously, both affecting the outcome of the experiment. This could provide input to theorists who are trying to reconcile quantum mechanics with general relativity and come up with a theory of quantum gravity.