I have used both Joomla and WordPress, and I prefer Joomla (and it could accomplish your task).
I made a post about it a while back:
Made a Joomla Website
(since the website link is no longer in my sig, it's
North American DotA Syndicate)
Anyways, I had a restricted area on the website for a while.
Since Joomla does not (yet) have customizable user ranks, you can use "Author" as your premium member skin, since it has the least power (essentially none) of any special rank.
Make the category/section you want restricted to Special, but still visible to anyone (so they know it's there). People will end up getting 403 - Forbidden errors when trying to access the page, so what I did is I made a custom 403 page (and a custom 404 page, but that's not relevant for this) that said something like, "Restricted area. If you are trying to reach the premium content area, you must be a subscriber. Link: asdfasdfsf)
Here's how to create a custom error page (replace the 404 with 403) if you want to do it that way:
How to create a custom 404 error page
Otherwise, you don't need that if you just make the premium content only VISIBLE to your subscribers, but then people might not know that they're missing something.
That was my solution - let me know if you have other ideas... I find Joomla pretty interesting (and amazing).