We address the question of to what extent the behavior of the Szlenk derivations of the dual unit ball of a Banach space determines the space up to an~isometric isomorphism. It was shown by C\'{u}th, Dole\v{z}al, Doucha, and Kurka (\textit{J.~Inst. Math. Jussieu}, 2024) that the form of the Szlenk $\varepsilon$-derivations of the unit ball of $c_0^*$ characterizes $c_0$ up to isometric isomorphism among all separable $\mathscr{L}_{\infty,1+}$-spaces. We investigate a similar question for a separable Hilbert space and, more generally, the spaces $\ell_p$ for $1 < p < \infty$. Since, as we will show, the shape of the Szlenk derivations fails to characterize these spaces among all Banach spaces, we restrict our attention to the class of sequence Orlicz spaces and obtain positive results within this class. This is based on a joint work with Marek Miarka.