We show that, within the perturbative regime, the constraining power of field-level inference on cosmological parameters is comparable to that of a joint power spectrum and bispectrum analysis based on the same perturbative model. We further examine the role of the field-level likelihood and demonstrate that using a Gaussian field-level likelihood to fit mock data with non-Gaussian noise leads to significant biases in the inferred cosmological parameters. In contrast, the joint power spectrum and bispectrum analysis can reliably recover the input cosmological parameters under a Gaussian likelihood, owing to the central limit theorem. These results underscore that the success of field-level inference critically depends on employing the correct likelihood, which may be the main obstacle to extending this method to smaller scales, even within the perturbative regime.