If you trade BTC for ETH, and then later trade that ETH back to BTC, then an adversary who was watching you might be able to link up your trades across the two public blockchains and therefore track what you did. They can look for an ETH transaction of an identical value to the BTC transaction you made occurring around about the same time, and then be able to make a reasonable guess as to which ETH are now in your possession. They can repeat this again in reverse to link your new bitcoin to your old bitcoin. This is impossible with Monero.

You also have to consider how you interact with the Ethereum blockchain. The most popular Ethereum wallets, such as MetaMask or multi-coin wallets, are in no way private, and harvest lots of data include your IP address, crypto addresses, and balances and transactions. Monero, on the other hand, can either be run via your own node or connecting to another node via Tor to mitigate these risks.