Template Attacks and the Stochastic Model provide advanced methods for side channel cryptanalysis that make use of `a-priori' knowledge gained from a profiling step. For a systematic comparison of Template Attacks and the Stochastic Model, we use two sets of measurement data that originate from two different microcontrollers and setups. Our main contribution is to capture performance aspects against crucial parameters such as the number of measurements available during profiling and classification. Moreover, optimization techniques are evaluated for both methods under consideration. Especially for a low number of measurements and noisy samples, the use of a T-Test based algorithm for the choice of relevant instants can lead to significant performance gains. As a main result, T-Test based Templates are the method of choice if a high number of samples is available for profiling. However, in case of a low number of samples for profiling, stochastic methods are an alternative and can ...