picasaweb.google.com and links directly to any Google site; as Picasa and Picasaweb are Google products. The icon to the right is the downloadable and free Picasa software for one's personal computer and the albums are not synched to the web automatically. It is generally easier to put slideshows together in a Google site through Picasaweb than Dropbox.
Dropbox is a web application, a personal computer application, and a phone app. What you do in one platform updates automatically in all the others. You can link individual images to Dropbox very easily and the platform is drag and drop for adding images. Images taken or scanned from one's phone are very easy to manage and maneuver around on Dropbox.