  Quantitative characterization of galaxy morphology is vital in enabling
comparison of observations to predictions from galaxy formation theory.
However, without significant overlap between the observational footprints of
deep and shallow galaxy surveys, the extent to which structural measurements
for large galaxy samples are robust to image quality (e.g., depth, spatial
resolution) cannot be established. Deep images from the Sloan Digital Sky
Survey (SDSS) Stripe 82 co-adds provide a unique solution to this problem -
offering $1.6-1.8$ magnitudes improvement in depth with respect to SDSS Legacy
images. Having similar spatial resolution to Legacy, the co-adds make it
possible to examine the sensitivity of parametric morphologies to depth alone.
Using the Gim2D surface-brightness decomposition software, we provide public
morphology catalogs for 16,908 galaxies in the Stripe 82 $ugriz$ co-adds. Our
methods and selection are completely consistent with the Simard et al. (2011)
and Mendel et al. (2014) photometric decompositions. We rigorously compare
measurements in the deep and shallow images. We find no systematics in total
magnitudes and sizes except for faint galaxies in the $u$-band and the
brightest galaxies in each band. However, characterization of bulge-to-total
fractions is significantly improved in the deep images. Furthermore, statistics
used to determine whether single-S\'ersic or two-component (e.g., bulge+disc)
models are required become more bimodal in the deep images. Lastly, we show
that asymmetries are enhanced in the deep images and that the enhancement is
positively correlated with the asymmetries measured in Legacy images.
