This question is motivated purely by curiosity. In algebraic geometry there is a major distinction between the world of characteristic $0$ and that of characteristic $p > 0$ with different methods, different results available etc.
From reading a number of books and papers I got the idea that in the case of rigid analytic geometry the distinction between the two worlds is not that important. So my question is:
Are there results in rigid geometry that are only known to be true in characteristic $0$ (like Hironaka desingularisation in algebraic geometry), or vice-versa, results that are only known to be true in positive characteristic?