  We assess the robustness of $\Lambda$CDM results from the full-shape analysis
of BOSS power spectrum using the one-loop prediction of the Effective Field
Theory of Large-Scale Structure (EFTofLSS). The public likelihoods PyBird and
CLASS-PT lead to results in agreement only at the $1\sigma$ level, despite the
fact that they are derived from the same BOSS dataset and theory model. We
perform a thorough comparison of the various analyses choices made between the
two pipelines, and identify that the differences come from the choice of prior
on the EFT parameters, dubbed "West-coast" (WC) and "East-coast" (EC) prior,
respectively associated to PyBird and CLASS-PT. In particular, because
posteriors are non-Gaussian, projection effects from the marginalization over
the EFT parameters shift the posterior mean of the cosmological parameters with
respect to the best-fit up to $1\sigma$ in the WC prior and up to $2\sigma$ in
the EC prior. We quantify that best-fit cosmological parameters extracted from
BOSS given the two prior choices are consistent at $\sim 1\sigma$. The
consistency improves to $\sim 0.5\sigma$ when doubling the prior widths. While
this reveals that current EFT analyses are subject to prior effects, we show
that cosmological results obtained in combination with CMB, or from forthcoming
large-volume data, are less sensitive to those effects. In addition, we
investigate differences between BOSS measurements. We find broad agreements
across all pre-reconstructed measurements considered ($<0.6\sigma$), but the
two available BOSS post-reconstructed measurements in Fourier space, once
combined with the EFT full-shape analysis, lead to discrepant Hubble parameter
$H_0$ at $\sim 0.9\sigma$. Given the various effects we discuss, we argue that
the clustering amplitude $\sigma_8$ measured with BOSS is not in statistical
tension with that inferred from Planck under $\Lambda$CDM.
