I hated every photo and video management in any OS. Even for Picassa, you can import your pictures into Piscassa, and then you have an alternative view of your pictures. The problem you never know where exactly the pictures are, which could be a real folder or something else. And many software don't deal with both pictures and videos, which is too bad as nowadays they come from the same cam.
The default image management software in Ubuntu is Shotwell. You can't fault it too much as it is built from 3rd party components.
The best thing is that when it imports pictures and videos from your cam. It put the images files into a tree of sub folders according to when the picture was taken, something like a top level folder of 2012, then subfolders for months, and then subfolders for days. You can change the behaviour. You can also re-import from a folder again into different arrangements.
You can publish to facebook, youtube, picassa, flickr etc but I haven't tried.
Imported pictures will not be imported again, which doesn't make much sense. If the picture files are identical, it doesn't matter. If not, it's rather complicated to tell them apart.
There are a few problems, but none that a little script cannot be solved.
When the date on your cam is wrong, you pictures may go everywhere that are difficult to find. Shotwell doesn't seem to be able to edit the timestamp in the exif metadata. You should use exiftool to shift the timestamp of all the pictures to get them corrected all at once before import.
Shotwell recognizes the default cam folder for pictures, but not videos. You need to use the import from folder feature for video, instead of import from cam.
Shotwell doesn't recognize .MPO 3D pictures nor .THM thumbnails. I use a simple script to change all the names to .mpo.jpg and .thm.jpg. Since they are all basically jpg files, Shotwell can read the exif metadata and import. MPO is two jpg images back to back for the left and right image. THM is the same as jpg to me.
To save download time from older cams, Shotwell will compares thumbnails to decide if the picture needs to be imported. The problem is that some cams have a .mpo file and a .jpg file for the same image. The .jpg file is just the left image for easy viewing. However, Shotwell is so clever as to ignore the filenames, timestamps, file sizes. Instead it only looks at the hash results of the thumbnail. So the .mpo and .jpg files have the same hash because the first half of the files are almost identical with the same thumbnail.
To import both .mpo and .jpg files of the same shot, you need to import from folder instead of import from cam. Whole files will be compared instead of just the thumnail.