All things equal Monero will always be more private than Bitcoin.

You are confusing anonymity (hidden identity) with privacy (hidden actions). You can have one without the other or both. Bitcoin can never be private it is a public blockchain. All actions are visible. The most you can hope to be is psuedonymous and obfuscate your actions - a weaker form of privacy that can be unraveled with more data or user mistakes (Monero's encrypted amounts and recievers are truly hidden.)

But even so, Bitcoin anon set is smaller than you let on. Because of it's default transparency this is an uphill battle for Bitcoin. Every single Monero user is automatically counted towards it's anon set by default. And ring signatures compound this over time without any action from those users at all. Vast majority of Bitcoiners don't coinjoin at all, let alone coinjoin every spend.

If a Monero user starts out KYC'd and withdraws this counts towards Monero's anon set. If a Bitcoiner does this they have to withdraw and have the additional step of coinjoining. It is also more expensive, slower, and more tedious.

Simple examples of each:

Bitcoin default transaction: Alice sent $X to Bob

Bitcoin coinjoin transaction: Maybe Alice sent $[X or Y] to [Bob or Charlie]

Monero transaction: Maybe Alice sent $[?] to [?]