Chain fees vary based on block space demand. The on chain fee rate is based on sats per byte. So a transaction that uses a lot of bytes on the blockchain to express the transfer will cost more.

An average on chain transaction is 300 bytes. But it can easily be more if you're sweeping a wallet with many UTXOs or spending from a multisig or complex script.

Lately, 1 sat per byte transactions have been confirmed within 10 mins to 1-week. So an average on chain transaction will cost 300 sats.

LN fees vary based on the route the payment takes. Each channel has a fee policy and your node software picks channels to route the payment based on many factors.

You could end up paying zero fees on LN if you're paying someone who you have a direct channel with. Or you could end up paying all kinds of extra fees depending on the LN wallet or custodial exchange you're using.

Additionally, fees on LN are measured in parts per million (ppm). A 1ppm fee on a channel means you will pay 1 sat fee for moving 1 million sats across that channel. Keep in mind you may have to use multiple channels to complete the payment. So if you send 1 million sats across 3 channels charging 1ppm fees, you'll pay 3 sats for the transaction.

There's also the issue of liquidity. No matter what, you're always able to send BTC to any address on chain. This isn't true for LN. It's possible that a payment path doesn't exist for the person you're trying to pay on LN. In that case, it doesn't matter how high your fee is, you still can't pay them. The fee is essentially "infinite" in this case.

With all this nuance aside, what's a good "rule of thumb" for when to use LN vs on chain today?

If we assume 1 sat per byte will always confirm, and we also assume the average fee on LN is 300 ppm (total per payment), then on chain fee equals LN fee at 1M sats.

Both these numbers are huge assumptions, and it could easily be way off. But at least it's a "ballpark figure".