I read that General Relativity and Quantum mechanics cannot both be correct? Which one seems more likely to be disproved at this point?

I heard there were fundamental incompatibilities between the two and as a result they cannot both be correct. Does this lead to any issues when basing a theory off of one or the other?

EDIT: [source] (http://www.infoplease.com/cig/theories-universe/quantum-mechanics-vs-general-relativity.html)