In image segmentation, level-set methods discriminating regions with Parzen estimates of their intensity distributions have proven useful in a broad variety of contexts. A number of area cost terms have been proposed to achieve this goal, such as log-likelihood, Bhattacharyya coefficient, Kullback-Leibler divergence and several others. In this work we compare the performance of the most widespread criterions and show that log-likelihood and assimilated methods have a clear advantage in terms of robustness. In particular, the other methods tested suffer from a boundary instability due to small region/small initialization/hard to distinguish regions. We also give some theoretical arguments supporting our experimental results on synthetic and real images.