It has been suggested recently that it is a reasonable abstraction of evolutionary processes to use evolutionary algorithms that select individuals based on the novelty of their behavior instead of their fitness. Here we study the performance of fitness- and novelty-based search on several neuroevolution tasks. We also propose several new algorithms that select both for fit and for novel individuals, but without weighting these two criteria directly against each other. We find that behavioral speciation, behavioral near neutral speciation, and behavioral novelty speciation perform best on most tasks. Pure novelty search, as well as a number of hybrid methods without speciation mechanism, do not perform well on most tasks. Using behavioral criteria for speciation often yields better results than using genetic criteria.