Well, I recently was browsing through some photos that were from some people in my orchestra, and I seem to be constantly getting these bloody proxy errors...This is why I'm making this comparison. Overall webshots, is a normal photo sharing environment, with a hard limit on photos, standard albums, and is also owned by Cnet. The things I can pick at is that the servers that Webshots is hosted on have been recently been flaky, and the fact that there isn't other was of labeling photos like tags or other things that, Flickr has, to search photos in many different ways. Overall, I have not seen why Webshots is so popular with people of my age, other than possibly simplicity of uploading photos and adding descriptions. This is not to say that uploading photos to flickr isn't just as easy, but Flickr has not been around as long as Webshots has. Word of mouth from what I've seen is how it has become more popular with people of my age. Another thing is that the search engine for finding photos is really poor, because of not having tags, only able to search descriptions and titles, and that does not turn out as much accurate answers as say Flickr's search is.
Flickr on the other hand, may be a tad harder to upload photos, with having to add tags, description, and title, and if you want it in a photoset, but it's more flexible. Photos can be put into multiple "sets", which are just collections of photos that have a similar reason. Tags can be browsed individually, allowing people to see photos from multiple sets, and ones that are not in sets. Flickr also has the additional community features, that allow people to make groups for similar interests that include photos, groups, and other things. Flickr is more than photo sharing, it includes the searching of photos, the commenting of them, as well as its flexible organizing. The disadvantage of a free Flickr account is that, the upload is capped at 20 megs. Though the advantage of this is that they only limit you on bandwidth, not on the total size of the photostream. Another disadvantage of a free account, is when you hit 200 photos, older photos are not shown in the photostream; they are not deleted though, they are just archived. Though compared to a paid Webshots account ($2 a month) to a Flickr pro account ($25 dollars a year), the Flickr pro account seems the better bargain, because you only have to pay once a year, though the 2 dollars a month equals about the same as the pro Flickr account. The additional benefits of Flickr outweigh Webshots. Flickr Pro has a 3 gig photo upload limit per month, and unlimited photos, as well as allowing images to be replaced with a different version after upload.
If your looking for a place to upload photos, and have a large amount of them, and upload a lot, then a Flickr pro account is the best way to go. If you just occasionally upload photos, or just dump a few occasionally for friends and family to see, then something like Webshots, or another free imagehost like image dump, may be the way to go, for the better free accounts. In my opinion, I would go always with Flickr for its organization, as well as its open API that allows you to use your photos in a variety of ways outside of flickr in other programs, and online services.