It's interesting how people talk about Monero as if we know for sure the privacy achievable in Monero is greater than the privacy achievable in Bitcoin.
Has anyone measured it?
Yes, Monero's privacy has been "measured" (if by "measured" you mean 'mathematically proven') and we thus do know for sure it's better than Bitcoin's.
https://downloads.getmonero.org/whitepaper_review.pdfSome of the privacy of Monero would be achievable using Bitcoin, but only if
everyone changed their operational security methods.
JustusRanvier uses stealth addresses, which privacy would be further improved if he only transacted with others who also do this. Ring signatures can also theoretically be accomplished albeit with some difficulty by using a client that could support this sort of key signing exchanges.
The problem for privacy remains, however, that since these are not a fundamental part of the protocol and a default for each transaction. There are limits to the amount of privacy that can be obtained in the face of correlation analysis by a well funded reveal-er of such secrets.
The only real argument I've seen for Monero is that privacy was make "at the protocol level".
In Monero's case though, "at the protocol level" simply means that everyone is forced to transact in a certain manner (a manner that mixes) on top of a bitcoin style address protocol.
However, this is not a real innovation. The exact same mixing procedures can be done on top of Bitcoin. No Bitcoin does not force this mixing, but any group of people, entities or wallets can agree to use the same mixing procedures as Monero
or better ones as they are developed. This means Bitcoin in the end will have better mixing/privacy features than Monero, since Bitcoin is flexible and any mixing procedure can be run on top of it.
Which brings us back to the Monero innovation, Monero's "innovation" is
simply the decision to force all transactions to use a single fixed mixing routine. That is not an innovation though, it is a decision.
Any group of entities using Bitcoin can make the same decision."At the protocol level" simply means that all transactions are forced into a single static mixing routine. However with Bitcoin, although people are not forced into any mixing routine, they are free to agree to use any mixing routing that may be developed.