I think there are multiple kinds of "neuromorphic" processors and they all have different abilities. OP pointed out the power efficiency. Researchers also work on analog chips which don't have the same constraints as traditional circuits.

But how / if you can truly use some of these differences depend on the use case, it would seem logical that well-exploited neuromorphic processors would be more power efficient, but it doesn't mean you have the algorithm to exploit it better than current processors for your use case, or that it's necessarily true. For complex tasks, we don't have a proof that would say "No algorithm on a traditional processor can outpeform the best algorithm we would know on a neuromorphic chip for the same power efficiency".

The main difference is that neuromorphic chips are still experimental, and that traditional chips allowed 10+ years of very fast progress in AI.