I vote for Picasa Web. I uploaded the high resolution versions of the images that appear in this Blog and it went quite quickly. You can find those images here. I couldn't do that in the same period of time with Flickr.
Interesting, the Blog application used Picasa Web without my knowledge as a place to store the images I post. This is not surprising, since Google and Picasa are partners. You can find this album here.
Also interesting is Picasalino, an iPhone App that uploads photos from your iPhone to a directory on Picasa called "Working". You may find that here. (If, of course, the permissions are set appropriately in all of these cases! We'll find out.)