Paper money is private. Bitcoins are public (connecting wallets to people is a challenge but with whole Internet tapped, maybe not a huge challenge).

Hence the "(depending on how you acquire/spend your bitcoins or cash)". With bitcoin it is much harder to keep your identity unconnected from your wallet (particularly if you want to do anything with it), though it is possible.

If one considers that the vast majority of people don't go through the lengths to remain pseudonymous on the web, connecting identities to wallets will (eventually) be trivial for the mainstream. However, I find it the case that as of now, that is inversely proportional to the people that use bitcoin. Not to mention all the laundry services out there or that could be placed on the front end of services used through tor (and possibly meshnets in the future).

And just as with cash income, attempting to launder bitcoin income turns it from a fine for undeclared income to a prison term for money laundering/intentional tax evasion.