> uses a more power efficient mining algorithm

Thats axiomatically impossible. Its the amount of energy required, not nhashes/etc, that disincentivize an attacker from rewriting history.

I think a combination of both is required for optimal results. Lightning is good enough for micropayments. On chain transactions are good for large payments. The only problem with on-chain scaling is that keeping a payment history for the entire planet is not really feasable. You have to somehow prune old data from the blockchain.