Before December, Tribble was the server used for long-term testing of new systems that will undergo several rounds of tweaking (DOffs, dilithium economy, skill revamp), while Redshirt was the short-term "Let's make sure this doesn't create a Negative Space Wedgie before we put it on Live" server (new ships and so on).
At present, it seems the roles continue. (Tribble just got the Ground Skill revamp for testing, while there's nothing on the immediate horizon for Redshirt right now, as Cryptic is going into Holiday mode for the next week or so.)
redshirt used to be a back up server used for closed builds and internal testing. it got used for the closed beta foundry last year for example. it was not made available to everybody all the time. just when they needed it or wanted a few select people.
tribble was the test server and would have 99% of the test stuff that was not super secret and anyone could use. any build that went on tribble would be on holodeck with 3 weeks or less.
when free to play builds started appearing, they knew it would require a couple of months of testing, but there would probably need to be updates to the game in the mean time. they could not use tribble as you cant just push bits and pieces so they opened up redshirt to everybody for any small builds that need to happen (urgent bug fixes etc).
most likely after f2p is launched redshirt will go away until they need it for the next super secret project that needs a small group of closed beta testers.