Via the geometric Satake correspondence, the Mirkovic-Vilonen cycles give bases for representations of semisimple Lie algebras. Similarly, by work of Lusztig, generic preprojective algebra modules give bases for these representations as well. It is a long-standing open problem to compare these bases. We will explain a new geometric way to make this comparison. As an application, we will show that these bases do not agree in SL_6.