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Huh, I might misunderstand it, but that property appears to be broken in account-based cryptocurrencies like Ethereum. Since there's no concept of unspent outputs, what could protect ETH etc users in a similar way? Wallet transaction index?

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There's a nonce on each account. If you see a transaction from the same account with the same nonce it's a double spend . Nonce can't be skipped either, so a double spend requires two transactions with the same nonce.

It is broken in Ethereum. In Ethereum, since consistency is enforced by transaction nonce rather than UTXOs, there is no way for a "watcher" to keep the payer honest by rebroadcasting a previously signed transaction output. Indeed, in Ethereum you can "cancel" a transaction in the mempool by signing a blank transaction with a higher fee and same nonce, which is by design.

Mind you that a tx in the mempool has not yet produced any changes to state. In BTC you can also replace-by-fee for instance (https://en.bitcoin.it/wiki/Transaction_replacement).

This page (https://github.com/ethereum/wiki/wiki/Design-Rationale) contains a good overview of the UTXO vs Account model with each's strengths and weaknesses.

How does Bitcoin decide which of the two transactions spending the same UTXO to pick?

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