When two phases of water are at equilibrium, the ratio of hydrogen isotopes in each is slightly altered because of their different phase affinities. This isotopic fractionation process can be utilized to analyze water's movement in the world's climate. Here we show that equilibrium fractionation ratios, an entirely quantum mechanical property, also provide a sensitive probe to assess the magnitude of nuclear quantum fluctuations in water. By comparing the predictions of a series of water models, we show that those describing the OH chemical bond as rigid or harmonic greatly overpredict the magnitude of isotope fractionation. Models that account for anharmonicity in this coordinate are shown to provide much more accurate results because of their ability to give partial cancellation between inter- and intramolecular quantum effects. These results give evidence of the existence of competing quantum effects in water and allow us to identify how this cancellation varies across a wide-range of temperatures. In addition, this work demonstrates that simulation can provide accurate predictions and insights into hydrogen fractionation.