I've gathered data from the last two bull runs to check how the transaction fees for sending BTC and ETH in their respective main nets have evolved.

I've defined the start of the bull run at the date of BTC's halving and the end of the run at BTC's respective ATH. I did this because I believe the halving is what has started runs in the past: supply is shortened whereas demand remains the same or increases. News outlets start posting about BTC, more people join in, the price grows once more and then we hit headlines. FOMO then kicks in.

2016-2017 run: sending ETH was ~14.3x cheaper

BTC halved on the 9th of July of 2016 and reached its ATH of $19,864 on the 18th of December of 2017. Here's a look of the fees in the period:

https://preview.redd.it/iwnrfeh5kuua1.png?1800&format=png&auto=webp&s=acb36aeb73c2c4964264f71f8ed2c599abdf24c1

• Average ETH transaction fee: 0.16 USD
• Average BTC transaction fee: 2.34 USD

2020-2021 run: sending ETH was ~1.43x more expensive

BTC halved once more the 11th of May of 2020 and reached its ATH of ~$69k on the 10th of December of 2021. Here's a look of the fees in the period:

https://preview.redd.it/hb5aulx2luua1.png?1800&format=png&auto=webp&s=cdda9fd62054b67ee901a28f1cdd645323b10a20

• Average ETH transaction fee: 8.14 USD
• Average BTC transaction fee: 11.65 USD

We can see that in the April/May 2021 peak the fees were pretty similar, whereas for in the second peak of this run ETH's value was one order of magnitude higher.

It was interesting to see that the correlation in the second peak of this run almost vanishes when compared to the first.

Notes

• These are average values, so one can't take many conclusions, as the volatility for txn fees was really high. In addition, the price of the coin directly relates to the USD-converted fees one must pay;
• The difference between BTC's maximum txn. fee between the runs is ~2.5x, i.e. maximum txn. fee in the 2020-2021 run was 2.5x higher than the one of 2016-2017;
• The Ethereum's network data is defined as "the daily average amount in USD spent per transaction on the Ethereum network". I'm not sure to what extent transactions in layer2 chains are accounted for. If that's the case, it's good on ETH: all smart contracts, NFTs and such transacted have a txn fee not very far from BTC's;
• Considering that one wants to send monetary value, though, I'd still use BTC over ETH on Ethereum's main net.
• Data was fetched from Nasdaq and Etherscan.

TL;DR

See charts, this was just a fun exercise.