I've had my pool for 1.5 summers, and used BBB exclusively. I have an autocover for any time the pool isn't in use, and typically only need to add 14 oz of chlorine a day to stay around my 3-4 ppm chlorine target. I'm a "data guy", and generally measure chemistry daily (and maintain a spreadsheet to record anything put into my water). I've found BBB to work well- very economical, consistent pH, and crystal clear water.
With that as background, I have to say that I was disappointed to see that my liner had indeed faded below the water line following the first full summer of operation. Not terrible, but very noticeable once I drained 6" water out for closing. There's no question- some fading occurred.
Now, the question: would it have faded the same/more/less had I used trichlor tabs, etc? I can't answer based on any experiences of my own. But, I will say that my pool guys (who are generally oblivious to anything other than trichlor for most of their customers) said they thought my liner fading was "normal".
IMO- anyone who says liquid chlorine will PREVENT fading isn't being honest. That doesn't mean it isn't the way I'd still operate a pool, though.