Determination of the maximum tolerated dose (MTD) is the main objective of phase I trials. Trials are typically carried out with restricted sample sizes. Model-based approaches proposed to identify the MTD (including the Continual Reassessment Method or CRM) suppose a simple model for the dose-toxicity relation. At this early stage of clinical development, the true family of models is not known and several proposals have been done. Asymptotic convergence of the recommendation to the true MTD can be obtained with a one-parameter model even in case of model misspecification. Nevertheless, operating characteristics with finite sample sizes can be largely affected by the choice of the model. In this paper, we evaluate and compare several models in a simulation framework. This framework includes a large class of dose-toxicity relations against which to test the competing models, an 'optimal' method that provides efficient non-parametric estimates of the probability of dose limiting toxicity to serve as a benchmark and as a graphic representation. In particular we explore the use of a one-parameter versus a two-parameter model, we compare the power and the logistic models and finally we investigate the impact of dose recoding on the operating characteristics. Comparisons are carried out with both a likelihood approach and a Bayesian approach for model estimations. We show that average performances of a one-parameter model are superior and that the power model has good operating characteristics. Some models can speed up dose escalation and lead to more aggressive designs. We derive some behavior related to the choice of model and insist on the use of simulations under several scenarios before the initiation of each new trial in order to determine the best model to be used.