From what I can gather, Guilty Gear is older, but BlazBlue came to prominence first. For a while, GG was stuck in cult classic-ville, and the rights were stuck with Sammy. This forced ArcSys to make a spiritual successor instead, which they did by taking their RPG idea and turning it into what is now BlazBlue. Apparently, it help revitalize interest in fighting games, alongside Street Fighter IV. That being said, Guilty Gear has been rapidly gaining in popularity, thanks to Xrd, ArcSys gaining popularity through FighterZ, and the reveal or Strive. From the looks of it, BlazBlue's receding for Guilty Gear to take hold. My bet's on SOl, but it's possible ArcSys and/or Nintendo could decide the era of BlazBlue isn't over just yet.