  Multi-conjugated adaptive optics (MCAO) yield nearly diffraction-limited
images at 2$\mu$m wavelengths. Currently, GeMS/GSAOI at Gemini South is the
only MCAO facility instrument at an 8m telescope. Using real data and for the
first time, we investigate the gain in depth and S/N when MCAO is employed for
$K_{\rm s}$-band observations of distant galaxies. Our analysis is based on the
Frontier Fields cluster MACS J0416.1-2403, observed with GeMS/GSAOI (near
diffraction-limited) and compared against VLT/HAWK-I (natural seeing) data.
Using galaxy number counts, we show that the substantially increased thermal
background and lower optical throughput of the MCAO unit are fully compensated
for by the wavefront correction, because the galaxy images can be measured in
smaller apertures with less sky noise. We also performed a direct comparison of
the signal-to-noise ratios (S/N) of sources detected in both data sets. For
objects with intrinsic angular sizes corresponding to half the HAWK-I image
seeing, the gain in S/N is 40 per cent. Even smaller objects experience a boost
in S/N by a up to a factor of 2.5 despite our suboptimal natural guide star
configuration. The depth of the near diffraction limited images is more
difficult to quantify than that of seeing limited images, due to a strong
dependence on the intrinsic source profiles. Our results emphasize the
importance of cooled MCAO systems for $K_{\rm s}$-band observations with
future, extremely large telescopes.
