I think that image file URLs are best and this is why:

* Base64 Strings and Files might have the same quality if your string is a encoded version of your image file
* Base64 Strings are much bigger than binary files (Usually 33% bigger) - http://davidbcalhoun.com/2011/when-to-base64-encode-images-and-when-not-to
* You only need Base64 when delivering the image using channels that are 7-bit encoded like emails, text files, CSS, HTML or other medium that only allows lower ascii characters.
* Gzipped images have the shortest size and pure binary image files are the faster to decode/display