A public blockchain can't be more private than Monero.
Recievers and amounts don't even appear on Monero's blockchain. They are completely hidden. Senders and transaction IP is obduscated. There is no transaction graph connecting senders and recievers on Monero. And amount analysis isn't possible either.
Monero transaction:
~6% chance Alice sent $[?] to [?]
Bitcoin transaction:
Alice sent $X to Bob
With coinjoin you are obfuscating everything, but all range of connections and amounts are visible. You can be deobfuscated with future data. There is a whole industry around it: blockchain analysis.
You are right though that they are specializing for 2 different goals. Bitcoin is trying to be sound money. Monero is trying to be digital cash. You can save with Bitcoin, and spend with Monero. Doing this virtually eliminates any worries about saving Monero.
