  We present a comparison of two methods for cosmological parameter inference
from supernovae Ia lightcurves fitted with the SALT2 technique. The standard
chi-square methodology and the recently proposed Bayesian hierarchical method
(BHM) are each applied to identical sets of simulations based on the 3-year
data release from the Supernova Legacy Survey (SNLS3), and also data from the
Sloan Digital Sky Survey (SDSS), the Low Redshift sample and the Hubble Space
Telescope (HST), assuming a concordance LCDM cosmology. For both methods, we
find that the recovered values of the cosmological parameters, and the global
nuisance parameters controlling the stretch and colour corrections to the
supernovae lightcurves, suffer from small biasses. The magnitude of the biasses
is similar in both cases, with the BHM yielding slightly more accurate results,
in particular for cosmological parameters when applied to just the SNLS3 single
survey data sets. Most notably, in this case, the biasses in the recovered
matter density $\Omega_{\rm m,0}$ are in opposite directions for the two
methods. For any given realisation of the SNLS3-type data, this can result in a
$\sim 2 \sigma$ discrepancy in the estimated value of $\Omega_{\rm m,0}$
between the two methods, which we find to be the case for real SNLS3 data. As
more higher and lower redshift SNIa samples are included, however, the
cosmological parameter estimates of the two methods converge.
