The matter power spectrum as derived from large scale structure (LSS) surveys contains two important and distinct pieces of information: an overall smooth shape and the imprint of baryon acoustic oscillations (BAO). We investigate the separate impact of these two types of information on cosmological parameter estimation for current data, and show that for the simplest cosmological models, the broad-band shape information currently contained in the SDSS DR7 halo power spectrum (HPS) is by far superseded by geometric information derived from the baryonic features. An immediate corollary is that contrary to popular beliefs, the upper limit on the neutrino mass m(nu) presently derived from LSS combined with cosmic microwave background (CMB) data does not in fact arise from the possible small-scale power suppression due to neutrino free-streaming, if we limit the model framework to minimal Lambda CDM+m(nu). However, in more complicated models, such as those extended with extra light degrees of freedom and a dark energy equation of state parameter w differing from -1, shape information becomes crucial for the resolution of parameter degeneracies. This conclusion will remain true even when data from the Planck spacecraft are combined with SDSS DR7 data. In the course of our analysis, we update both the BAO likelihood function by including an exact numerical calculation of the time of decoupling, as well as the HPS likelihood, by introducing a new dewiggling procedure that generalises the previous approach to models with an arbitrary sound horizon at decoupling. These changes allow a consistent application of the BAO and HPS data sets to a much wider class of models, including the ones considered in this work. All the cases considered here are compatible with the conservative 95%-bounds Sigma m(nu) < 1.16 eV, N-eff = 4.8 +/- 2.0.