Your best bet is to open IE for favorites, and Firefox, for bookmarks, on the old computer and 'Export' their favorites/bookmark lists to files. Then you can copy those files across and 'Import' them into the new computer's browsers.
What are Webshots?
I used The Tornado to transfer files from my old computer to my new. I have been able to find my music but can't locate my Webshots data, or my favorites/bookmarks. I have found the folders but they are all empty, even though they show by the size that they should contain files. Where can they be hiding?