They perform similar, but not identical functionality.The New Posts uses read tracking to determine which threads to show, but doesn't update upon reload of the page. Those results are cached as they are an individual search. If you need new results, you'll have to click the link again to perform a new fetch of posts.
Recent Posts doesn't use read tracking (it is the link provided to guests) to determine what posts to show in the listing. As with New Posts, it requires a click of the link to function and not a simple refresh.
Big mistake! The members went crazy!