Partly inspired by the following post: Relation and difference between time series and regression?
After thinking carefully into these two subjects, I kind of wondering for what kind of data/situation time series analysis is more suitable? (or conversely, stochastic processes will be more suitable) There are some examples (e.g. Auto-regression in the post cited above) where the time series are more suitable; but stochastic processes could as well depict them in terms of filtration. And in other examples (e.g. Poisson process) where stochastic methods dominates but it seems time series specialist in economics could analyze them equally well.
Therefore, is there an example that only one of these two methods works? (I know their relation are vague, so any comments are welcome.)