I, too have been amazed at the differences in gear and techniques between cavers and big wall climbers. Derek does a good job of explaining why the two sports use such vastly different ascending rigs.
The aid climbing/big wall technique is actually very efficient for... aid climbing and big walls. Caving single rope technique is very efficient for... single rope technique.
Frankly, I can't see how I would manage to follow a lead on an El Cap big wall using a rope walker system. Explain how you would expeditiously and efficiently ascend a slab, followed by a pendulum/traverse, followed by an overhang using a rope walker or a frog? And I can't see how I would manage to pull myself out of Fern Sink with my arms using a big wall rig. How is caving technique better at negotiating lips than climbing technique? I don't see a different, except that cavers are much more likely and willing than climbers to place bolts to optimize rigging and avoid lips.
However, there is definitely room for some shared information and shared technique. With just a little more gear, big wall climbers could make ascending considerably easier in certain conditions, such as ascending fixed ropes.
Cavers, though much more advanced than climbers in terms of ascending free-hanging ropes, have much to learn from climbers about dynamic loads, fall factors, and the like.
Finally, I agree that climbers haven't really accepted helmets. I think climbers have much larger egos than cavers. Helmets are simply not cool. That is, until you''ve had your bashed in by a rock. Wanna see my scar? I narrowly survivied that lesson back in 1978.
About 2,000 feet up the Muir Wall, El Capitan, 30 years ago