Intracellular transport via the microtubule motors kinesin and dynein plays an important role in maintaining cell structure and function. Often, multiple kinesin or dynein motors move the same cargo. Their collective function depends critically on the single motors' detachment kinetics under load, which we experimentally measure here. This experimental constraint-combined with other experimentally determined parameters-is then incorporated into theoretical stochastic and mean-field models. Comparison of modeling results and in vitro data shows good agreement for the stochastic, but not mean-field, model. Many cargos in vivo move bidirectionally, frequently reversing course. Because both kinesin and dynein are present on the cargos, one popular hypothesis explaining the frequent reversals is that the opposite-polarity motors engage in unregulated stochastic tugs-of-war. Then, the cargos' motion can be explained entirely by the outcome of these opposite-motor competitions. Here, we use fully calibrated stochastic and mean-field models to test the tug-of-war hypothesis. Neither model agrees well with our in vivo data, suggesting that, in addition to inevitable tugs-of-war between opposite motors, there is an additional level of regulation not included in the models.