The properties of precessing, coalescing binary black holes are presently inferred through comparison with two approximate models of compact binary coalescence. In this work we show these two models often disagree substantially when binaries have modestly large spins (a≳0.4) and modest mass ratios (q≳2). We demonstrate these disagreements using standard figures of merit and the parameters inferred for recent detections of binary black holes. By comparing to numerical relativity, we confirm these disagreements reflect systematic errors. We provide concrete examples to demonstrate that these systematic errors can significantly impact inferences about astrophysically significant binary parameters. For the immediate future, parameter inference for binary black holes should be performed with multiple models (including numerical relativity), and carefully validated by performing inference under controlled circumstances with similar synthetic events.