Never been in the BA lounge but the 3rd party lounge is 'interesting'.
It would be best described as like a staff break room that takes Priority Pass.
Last time I was there our group of 3 were the only customers who weren't uniformed airline staff. At least we had the booze to ourselves!
Also as, others have hinted there really is no such thing as 'airside' at TXL - you pass through security at the gate.