Invariant manifolds provide useful insights into the behavior of nonlinear dynamical systems. Spectral submanifolds are invariant manifolds that capture the behavior of non-conservative systems near an attractor (or repellor). Approximations of spectral submanifolds can be used to analyze the transient behavior of autonomous systems, but also to study the effect of non-autonomous forcing via forced response curves and backbone curves. Current approaches to computing approximations for spectral submanifolds rely on a parametrization of the manifold and the reduced dynamics on it via truncated power series. While this leads to efficient algorithms for recursively determining the coefficients of this parametrization, the problem itself is ambiguous in that there are fewer equations than unknown coefficients. Although this ambiguity is well known, it is rarely discussed and usually solved by introducing more equations, the effects of which have hardly been studied. We present a benchmark study to analyze the performance of three popular approaches to resolving this ambiguity: the graph style parametrization, the normal form parametrization, and the normal form parametrization for “near resonances”. We show that no parametrization is superior, and discuss how and why poor approximations of specific parametrizations are unexpected for certain benchmark systems. All approximations are limited by the radius of convergence of the truncated power series, which depends substantially on the chosen parametrization and cannot be determined a priori. Although not surprising, the investigations on the benchmark systems show how serious this influence is and what potential for improving the methodology can be found here.