Which criteria performs better?

As expected there is no concrete answer. A recent, fairly detailed, simulation study in the context of surface reconstruction from range data [6,5] shows that

• A moderate region size is crucial to the performance of all model selection criteria.
• The information theoretic criteria perform better than confidence interval based criteria.
• The bootstrap based criteria perform well, closely following the performance of their non-bootstrap versions.
• The Bayesian criteria (equation 1) performed the best in the experiments, closely followed by CAIC.
• AIC showed a strong bias towards higher order surfaces, while Rissanen's criteria showed a bias towards lower order surfaces.