What is going on with the fees and why is an ETH transaction more expensive than a Bitcoin transaction?
Not always, this varies from wallet to wallet, as well as according to the different exchanges, there are bitcoin wallets that have higher fees than Ethereum and the matter also differs between exchanges where there are exchanges with low fees and other exchanges with high fees.
Yes, commissions on various exchanges differ from each other. Two days ago, I had to withdraw Ethereum from the Poloniex and Binance exchanges. At the same time, the Commission with Poloniex was 0.01 ETH, and with Binance 0.004 ETH. But on the same day, the Commission for withdrawal to Myetherwallet.com it was even higher than on the specified exchanges.