The complexity of entire T cell receptor (TCR) repertoires makes their comparison a difficult but important task. Current methods of TCR repertoire comparison can incur a high loss of distributional information by considering overly simplistic sequence- or repertoire-level characteristics. Optimal transport methods form a suitable approach for such comparison given some distance or metric between values in the sample space, with appealing theoretical and computational properties. In this paper we introduce a nonparametric approach to comparing empirical TCR repertoires that applies the Sinkhorn distance, a fast, contemporary optimal transport method, and a recently-created distance between TCRs called TCRdist. We show that our methods identify meaningful differences between samples from distinct TCR distributions for several case studies, and compete with more complicated methods despite minimal modeling assumptions and a simpler pipeline.