(I did not want to sound like I was advocating for anything in particular, but since it would be on topic, and you kindly ask :)
As you said, as a start, anything with a higher TPS (transactions per second) is more efficient, which helps. Some notables, in my mind (not exclusive, of course) ...
I really love what Cartesi is doing: They are bringing Smart Contracts to the "linux stack", securely (same guarantees than on-chain) but -outside- of chain. This will, obviously, raise efficiencies ...
The Fantom chain is high performance -and- their contracts are Ethereum-compatible (smart!), aside from it being a very nice, well thought out "ecosystem"
The NANO token makes it a point of pride, exactly how -much- more efficient ("Eco-friendly") it is than BTC, and their approach is interesting. (It has got some HN love lately and everything :)
(On a tangent, I am also a fan of what FRAX is doing in the stablecoin space, bringing decentralization and transparency to that space ("Frax is the world’s first fractional-algorithmic stablecoin") ...