If new physics has to be discovered in the forthcoming years, the ultimate goal of the high-energy physics program will consist of fully characterizing the newly-discovered degrees of freedom in terms of properties such as their masses, spins and couplings. I will show how the availability of polarized beams at high-energy proton-proton colliders could yield a unique discriminating power between different beyond the Standard Model scenarios giving the same final-state signature, and how polarized beams could be help us to obtain information on the parameters of the hypothetical new physics sector of the theory. I will discuss as an illustrative example the case of a particular class of models leading to monotop production, and explain how these models could be distinguished by means of single- and double-spin asymmetries in polarized collisions at a Large Hadron Collider operating at a center of-mass energy of 14 TeV and at the recently proposed Future Circular Collider.