If you want a better sample size of the default banners, look in
C:\Program Files (x86)\Steam\appcache\librarycache
Sigh, Steam is currently wasting 1.4GB of my drive space on a folder of banner and box images.
Anyway, looking there the banner background seems to be the “library_hero” files. It seems the standard resolution is 1920x620, though I do see one game in my library that has a 1024x550 resolution images instead.
The ‘box art’ images appear to be the “library_600x900” files, which appear to be either 600x900 or 300x450. Strangely enough, the higher resolution seems to be used only for images that appear to have been created automatically (taking the “header” image and filling the rest of the vertical space with a color smear), while the lower resolution is used for images that look like they actually had a person supplying art of the appropriate aspect ratio.