I discuss how much information on cosmological parameters can be extracted from a perturbative bias model at the field level after marginalizing over initial conditions, compared with summary statistics. I focus on three qualitatively different scenarios, all in the cosmic-variance-limited case. First, I show that the galaxy power spectrum plus bispectrum and the field-level modeling give comparable errors on the amplitude of the primordial power spectrum A_s after marginalizing over the linear bias and fixing all other biases to zero. I then prove that the error on any cosmological parameter present in the linear power spectrum is the same as in linear theory, if biases are known. That is, forward modeling does not suffer from complications coming from coupling between long and short modes that can instead affect summary statistics. Depending on the shape of the linear power spectrum, the damping of the BAO scale from displacements and the contribution from nonlinearities to the power spectrum covariance can be greatly enhanced: this degrades the constraints on the BAO scale and A_s, respectively, even if biases are perfectly known.