One notable difference is that the chrome version reworks the article pages, the skimmer appears to just frame them
TimesSkimmer was very good when it came out. But gradually, it has become very slow and somewhat unusable. I definitely think the Chrome version is much far ahead of the Skimmer. Skimmer used to open the article in an iFrame, which spoils the entire motive of decluttering. There were also needless animations that made it a bit slow. Plus the lack of any social functionality that made sharing articles difficult. I really like that they took care of all of these issues in the Chrome version!
By the URLs of some resources it looks like this is Skimmer 2.0 or something like that (e.g. http://graphics8.nytimes.com/webapps/skimmer/2.0/build/app-s...)
http://www.nytimes.com/timesskimmer/
But it's a good start.