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 from the Large Binocular Camera (LBC) on the Large Binocular Telescope (LBT). Having acquired over 30 hr of data (315 images with 5-6 minutes exposures), we generated multiple image mosaics, starting with the best atmospheric seeing images (FWHM less than or similar to 0 ''.8), which constitute similar to 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 less than or similar to 1 ''.8 (similar to 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 similar to 90% complete to U-AB less than or similar to 26 mag. Fainter than U-AB similar to 27 mag, 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) less than or similar to 32 mag arcsec(-2)) show a more gradual drop (10% between U-AB similar or equal to 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. We conclude that for studies of brighter galaxies and features within them, the optimal-resolution image should be used. However, to fully explore and understand the faintest objects, the deeper imaging with lower resolution are also required. Finally, we find-for 220 brighter galaxies with U-AB less than or similar to 23 mag-only marginal differences in total flux between the optimal-resolution and lower-resolution light-profiles to mu(AB)(U) less than or similar to 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.