crypto claims

Well, that depends on what claims you're interested in.

Monero solves the problem of replacing cash while preserving all of the anonymity of cash. Transactions are reasonably fast, fees are low, etc.

Bitcoin is a terrible currency IMO, and isn't much better as a store of value because:

• transaction fees are high - due to finite block size and frequency
• it's a huge target for speculation as the largest cryptocurrency
• transactions are slow (see first bullet point)

The problem Bitcoin is trying to solve is transparency of transactions, putting huge emphasis on the public ledger. That's always going to be at odds with a currency, where most people don't want their transactions tracked.