  Based on the cosmic shear data from the Canada-France-Hawaii Telescope
Lensing Survey (CFHTLenS), Kilbinger et al. (2013) obtained a constraint on the
amplitude of matter fluctuations of
$\sigma_8({\Omega_\mathrm{m}}/0.27)^{0.6}=0.79\pm0.03$ from the two-point
correlation function (2PCF). This is $\approx3\sigma$ lower than the value
$0.89\pm0.01$ derived from Planck data on cosmic microwave background (CMB)
anisotropies. On the other hand, based on the same CFHTLenS data, but using the
power spectrum, and performing a different analysis, Liu et al. (2015) obtained
the higher value of
$\sigma_8({\Omega_\mathrm{m}}/0.27)^{0.64}=0.87^{+0.05}_{-0.06}$. We here
investigate the origin of this difference, by performing a fair side-by-side
comparison of the 2PCF and power spectrum analyses on CFHTLenS data. We find
that these two statistics indeed deliver different results, even when applied
to the same data in an otherwise identical procedure. We identify excess power
in the data on small scales ($\ell>5,000$) driving the larger values inferred
from the power spectrum. We speculate on the possible origin of this excess
small-scale power. More generally, our results highlight the utility of
analysing the 2PCF and the power spectrum in tandem, to discover (and to help
control) systematic errors.
