Beatty's forces at Jutland included four Queen Elizabeth class fast battleships in addition to his battlecruisers. For most of the Battlecruiser engagement, the QEs were effectively out of action, strung out too far behind Beatty's BCs to support them. If Hipper were to stay and fight, the QEs could catch up and engage, which would likely go very badly for Hipper. The QEs were the newest class of BBs, and they had much heavier armor (max of 13 inches in the main belt, vs 6 inches or 9 inches for the various BCs) than Beatty's BCs, and they had significantly heavier guns (15-inch, vs 12-inch for most of the BCs or 13.5-inch for HMS Tiger).
IMO, the best opportunity for a better German outcome in the BC engagement at Jutland would be for Scheer to do a better job of springing the trap that Hipper had lured Beatty into by fleeing towards the main body of the HSF. Perhaps if Hipper had sent a destroyer or a seaplane ahead to alert Scheer that Beatty was coming, Scheer might have been able to deploy the HSF's BBs across Beatty's T. As it was, it took a fair amount of luck for Beatty's force to disengage and flee to the north without taking heavy losses, especially among the QE battleships, which had been too strung out to receive the order to turn back to the north.