Pretty much every single quantum mechanical experiment contradicts General Relativity. Take the double slit experiment. General Relativity predicts that Newtonian mechanics should hold in the double slit experiment, because General Relativity reduces to Newtonian mechanics in these approxomations.

So, the double slit experiment is one experiment that shows contradiction between the two theories.

Similarly, pretty much every observation in cosmology contradicts the Standard Model, because the Standard Model predicts no such thing as gravitation in its macroscopic limit.

Pretty much every single quantum mechanical experiment contradicts General Relativity. Take the double slit experiment. General Relativity predicts that Newtonian mechanics should hold in the double slit experiment, because General Relativity reduces to Newtonian mechanics in these approxomations.

So, the double slit experiment is one experiment that shows contradiction between the two theories.

Similarly, pretty much every observation in cosmology contradicts the Standard Model, because the Standard Model predicts no such thing as gravitation in its macroscopic limit.

EDIT I want to correct the last paragraph. The Standard Model can include an Effective Field Theory of Gravity, like explained here

This theory does reproduce General Relativity in the macroscopic limit. You could say that this theory accurately models all experiments until around the Planck scale.