Have a look at OpenPhoto (self installed or hosted, a la Wordpress). Lets you select where you want your photos to be stored (Dropbox, S3, etc) and provides web and mobile apps to access them. Also, completely open source[1].
Dropbox isn't really optimized for photos. It does a great job backing up and syncing across devices but that's about where it stops in relation to photos.
We provide a layer on top of Dropbox. You can better organize your photos using albums or tags. Metadata from your photos are automatically extracted (title, tags, geolocation). There's a proper photo API for creating and using additional apps. There's plenty more but the blog post[1] covers it well if you're curious or ping me :).