The exponential race model embodied in the theory of visual attention (TVA) and the power law generalization of the sample size model (SSPL) provide competing accounts of the mechanisms that determine how exposure duration, set size, and attention influence how many items enter visual short-term memory (VSTM). In the exponential race model, items compete for entry into VSTM in a processing race with exponentially distributed processing times. The most recent version of the sample size model assumes that target sensitivity measured by d increases monotonically as a function of exposure duration and decreases as a power function of set size. Here we compare the two models in a new experiment with letters and Gabor patches and with data from five previously published experiments. This was done by applying TVA to the two-alternative forced-choice method (2AFC), which forms the basis of the experimental work on the sample size model. Both models fitted individual participants' proportions of correct trials quite well, and overall the fits by the two models were almost indistinguishable. This was confirmed by formal pairwise comparison of TVA and SSPL by the Akaike information criterion and the Bayesian information criterion measures.