tl,dr: With current prices nano fees (electricity for PoW) are at least around 10x cheaper than btc lightning fees.
Today I tried a bunch of lightning transactions between wallets on my phone and tablet with channels open to different providers. Out of 18 transfers between 3 and 97000 sats in size, 8 succeeded within 3 s, 1 failed in 10 min and the rest are still in progress after 20-30 min. The fee for one was 100 sats and less than 20 for the rest, with couple of 1 and 2 sat transactions. With current btc price around 6 k€ that is at least about 1e-4 €.
Nano [seems](https://github.com/nanocurrency/raiblocks/blob/994100dc8229137e49d440bdb13fe7b5b2767104/rai/lib/work.hpp#L38) to be aiming for 5 s PoW for sending one transaction, which assuming 50 W CPU, or one core of CPU, would require 250 Ws = 250 J of energy. With electricity price of 0.1 € / kWh or 3e-8 € / J that would be about 7e-6 € worth of electricity, or at most about 10% of btc lightning transaction price, usually much less.