In a sign of the companies’ divergent fortunes, MySpace said on Thursday it will let its users log in to their Facebook accounts through their MySpace page.

Doing so will port the likes and interests they have listed on their Facebook profiles to MySpace, where they will get a stream of entertainment content based on these interests.

MySpace users have already been able to sync their status updates to their Facebook profiles. Thursday’s announcement is a deeper integration of Facebook’s technology into MySpace. It doesn’t involve any financial transactions.

The integration of Facebook Connect into MySpace’s home page will be followed by the addition of Facebook’s “Like” buttons across MySpace, the company said.

Once a rival, MySpace has conceded that it is no longer a social network but a social entertainment destination — think MTV for the Web 2.0 generation. To this end, the company recently overhauled its website to give its mostly young audience more ways to consume music, videos and celebrity gossip. CEO Mike Jones said in a conference call on Thursday that the users’ initial response to the redesign is “very, very positive.”

Facebook, meanwhile, is working to become the social overlay of the Web. Dan Rose, a Facebook vice president, called the integration with MySpace a “powerful demonstration of the Facebook platform.”