The Air Traffic Management system is heavily influenced by meteorological uncertainty, and convective weather cells represent one of the most relevant uncertain meteorological phenomena. They are weather hazards that must be avoided through tactical trajectory modifications. As a consequence of the existence in uncertainty in meteorological forecasts and nowcasts, it is important to consider the convective weather cells to be avoided as a stochastic, time-dependent process. In this paper we present a comparative analysis of two methodologies for handling stochastic storms in trajectory planning: one based on stochas- tic reachability and a second one, based on robust optimal control. In the former, the thunderstorm avoidance problem is modelled as a stochastic reach-avoid problem, consid- ering the motion of the aircraft as a discrete-time stochastic system and the weather haz- ards as random set-valued obstacles. Dynamic programming is used to compute a Markov feedback policy that maximizes the probability of reaching the target before entering the unsafe set, i.e., the hazardous weather zones. For the latter, the stochastic dynamics of the storms are modeled in continuous time. We implement an optimal control formulation that allows different possible realizations of the stochastic process to be considered. The resulting problem is then transcribed to a nonlinear programming (NLP) problem through the use of direct numerical methods. A benchmark case study is presented, in which the effectiveness of the two proposed approaches are analyzed.