hmm...to bad that Star Trek Phase II is already taken ;-)
How about introducing "years" or "era"?
Everything Roddenberry was involved in -> Star Trek: Roddenberry Years
Everything that has only BnB without Roddenberry Star Trek: Berman Braga Years
From 2009 up to the next big change -> Star Trek: Abrams Years
Do you even know what actually qualifies as "Berman Braga Trek"? Voyager seasons 5 and 6 and Enterprise. That's it, that's all the Trek Braga had any authority over. I suppose if you want to stretch it you could throw Generations and First Contact in there since he co-wrote the scripts with Ron Moore.
Still, there's 14 years of Prime Trek after Roddenberry died. True Berman was in charge all 14, but Braga only had any real authority for 6 of those years. That's less than half.
I don't want to sound like I'm flying off the handle, but it does get irritating always seeing everyone associating Braga with having more power than he really did.