Filesystem, of course, unless you're aiming for a story on thedailywtf. The easiest way is to have the photos organized by a property you can derive from the file itself, such as its SHA-1 hash. Then just store the hash in the database, attached to the photo's primary key and other attributes (who uploaded it, upload date, etc).
It's also a good idea to divvy up the photos on the filesystem, so you don't end up with millions of files in a single directory. So you'll have something like this:
storage/00/e4/f56c0de1c61fdb926e79e8a0a65bd12930c9.jpg
storage/25/9a/ec1c55bfb660548a6770238668c4b117d92f.jpg
storage/5d/d5/4b01d98f17a9ad9dd1526b49ba39b5aa37a1.jpg
storage/63/49/6f740b6c284ce6685dc17d473a7360ace249.jpg
storage/b1/75/066d178188dde110149a8422ab651b0ee615.jpg
storage/b1/20/a2b7d02b7b0c43530677ab06235382a37e20.jpg
storage/da/39/a3ee5e6b4b0d3255bfef95601890afd80709.jpg
This is also easy to port if you ever move to sharded storage.