I worked on a site that did this. We lost about 75% right away (after the couple free months they got for being early users). It took the site about a year to get people coming back and signing up for the fee based service.
You will lose a lot instantly, 25%. Then the other 50% take off as soon as the fees start. It will take about a year to get back to 50%.
Price also was a factor. We went from free to $5 bucks a month. The more expensive probably the sharper the drop off.
There is one site I visit quite often that generally has the best information in its industry. It was advertising based and was struggling. They started a premium section that had the same info except without advertising on the pages. They also had some unique content in the premium section and things like audio updates, special interviews, and things like that. They are now making more money from the premium subscriptions than they ever did with advertising.
I think the main key is the value added content that the premium members are receiving. If they went strictly to a subscription model they would probably lose most of their users but since they have the basic site and the premium site with the extra features people see the benefit of paying $40 per year.