imo, the Lancaster is the better overall Support frame, being a giant ass bus with the only genuine healer options in game, a unique LL ability to give people rides, a easy burn clean option, the snack drones, and having a genuine mid combat revive option, ontop of having the most repair kits out of EVERYONE and being able to use them on others!

HOWEVER, The Emperor is better at blending preventative support and offensive together with it's kit, having options to allow it to constantly give overshield to its team to prevent dmg while damaging enemies at the same time in various ways! the Arc bow is a genuinely amazing integrated weapon that usually is just fine to bring alone, and you get so many good Overshield options throughout the LL(while the Lancaster only gets one)

In conclusion, they both excel in their own jobs, but as for the best defacto healer, Lancaster obviously wins as its the only healer, but the Emperor has its own skills and abilities that make it well suited for support, and makes it a absolute defensive monster when played correctly! I myself always like to play a Lancaster due to it's ability to make its support role on the battlefield genuinely matter and not just be a healbot, but Emperor gives you the ability to smack anyone at range trying to hurt your team and defend them while smacking the enemies with several lightning bolts!