We present a study of the trade-off between depth and resolution using a large number of U-band imaging observations in the GOODS-North field (Giavalisco et al. 2004) from the Large Binocular Camera (LBC) on the Large Binocular Telescope (LBT). Having acquired over 30 hours of data (315 images with 5-6 mins exposures), we generated multiple image mosaics, starting with the best atmospheric seeing images (FWHM $lesssim$0.8), which constitute $sim$10% of the total data set. For subsequent mosaics, we added in data with larger seeing values until the final, deepest mosaic included all images with FWHM $lesssim$1.8 ($sim$94% of the total data set). From the mosaics, we made object catalogs to compare the optimal-resolution, yet shallower image to the lower-resolution but deeper image. We show that the number counts for both images are $sim$90% complete to $U_{AB}$ $lesssim26$. Fainter than $U_{AB}$$sim$ 27, the object counts from the optimal-resolution image start to drop-off dramatically (90% between $U_{AB}$ = 27 and 28 mag), while the deepest image with better surface-brightness sensitivity ($mu^{AB}_{U}$$lesssim$ 32 mag arcsec$^{-2}$) show a more gradual drop (10% between $U_{AB}$ $simeq$ 27 and 28 mag). For the brightest galaxies within the GOODS-N field, structure and clumpy features within the galaxies are more prominent in the optimal-resolution image compared to the deeper mosaics. Finally, we find - for 220 brighter galaxies with $U_{AB}$$lesssim$ 24 mag - only marginal differences in total flux between the optimal-resolution and lower-resolution light-profiles to $mu^{AB}_{U}$$lesssim$ 32 mag arcsec$^{-2}$. In only 10% of the cases are the total-flux differences larger than 0.5 mag. This helps constrain how much flux can be missed from galaxy outskirts, which is important for studies of the Extragalactic Background Light.
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