If you’re still seeing the old/current version, you can check out what’s coming by going directly to mobile.twitter.com.
Twitter Begins Rolling out ‘Lite’ Version of Website to Everyone. Twitter’s calling it the “new twitter.com”, but this update is clearly the lite variant of their website that mobile users have been using for over a year. Good on them for pushing this out to everyone—I’ve found it to be significantly faster and nicer to use than the normal site. It’s also (sadly) the best official way to use Twitter on your Mac.