Let \(\phi \,:\,\mathbb R\mapsto [0,+\infty)\) be an increasing and convex function. The Hardy--Orlicz space \(H_\phi(B)\) in the unit ball \(B\) of \(\mathbb C^n\) is defined as the space of functions \(f\) holomorphic in \(B\) and such that \(\phi(\log| f| )\) possesses a harmonic majorant in \(B\). The Bergman--Orlicz space \(A_\phi(\nu_\alpha)\) is defined by the requirement \[ \int_B \phi(\log| f(z)| )\,d\nu_\alpha(z) -1\), and \(d\nu\) is the Lebesgue measure in \(B\). The author obtains alternative characterizations of the spaces \(H_\phi(B)\) and \(A_\phi(\nu_\alpha)\). For the space \(H_\phi(B)\), this characterization reads as follows: \(f\in H_\phi(B)\) iff \[ \int_B \phi''(\log| f(z)| )\,\frac{| Df(z)| ^2}{| f(z)| ^2} \,(1-| z| ^2)\,d\nu(z)<+\infty, \] where \(Df(z)=\widetilde\nabla f(z)/(1-| z| ^2)\) and \(\widetilde\nabla\) is the invariant gradient. Similar characterizations with \(D\) being the radial derivative or complex gradient were known before. As an application, the author obtains new characterizations of the classical Nevanlinna, Hardy, and Bergman classes in the ball.