My vote goes to Dead or Alive, I liked Blazblue also. However the thing that is frustrating with Blazblue is there is one save file and you can not erase it. Dead or Alive also has just one save file but at least you can reset it.
I've replayed Dead or Alive a few times, meanwhile Blazblue sits around collecting dust since I've completed it. --- With your bad back, I don't think you should be picking up any girls. I went ice fishing the other day and all I caught was a cold.
To me BlazBlue is the real winner, even without online play the game is so full of content and unlockables and the fighting engines is smooth and fun to master, Super Street Fighter IV 3D on the otherhand is just cheap. Everything in that game is just overpower, you get by too many hits you earn an Ultra, you do too many hits you earn a Super. It's just too overbalanced.