I'm "spinning my wheels" on the fact that one cryptocurrency supports a public consensus audit of its veracity. The other does not.
You are completely spinning your wheels.
Both allow that, if the cryptographic functions check out. Both do not, if the cryptographic functions do not check out.
It appears I need to spell this point it out.
Lets then consider a random sample group of 3 addresses and 3 transactions between those addresses (resulting in 6 corresponding balance movements). I'm going to audit the blockchain for that sample group using bog standard auditing techniques that any industry seasoned auditor would recognise - regardless of their familiarity with 'cryptocurrencies'.
The bitcoin-spending public does this intuitively every day on blockchain.info et al. I'm just presenting a formal version of what they do here to quantify the process.
We'll create a full set of accounts as analogues to the blockchain addresses - i.e. the asset (balance sheet) perspective, the turnover (income/expense) perspective and the detailed transaction history.
First: The asset accounts (our 'balance sheet detail') is basically just what you can find on any public-consensus blockchain explorer such as blockchain.info.
Next: The income and expenditure statements which may have been compiled from our own records.
Finally: We combine the balances from each of the perspectives above into a single "trial" balance. This will tell us if there are discrepancies amongst our own records, what the wallet tells us, what blockchain.info tells us and what we understand the transaction history to have been:
So my trial balance balances and Bob's my Auntie Alice this time. Debits equal credits and I can go and feed the cat.
Now try doing that on a cryptonote blockchain. You're screwed. Half the data isn't available. Even if you're only checking your own transactions you can't do such an audit because you cannot construct a trial balance - and CONCLUSIVELY not for a random set of addresses. You may have most of the information in the income statement but not the balances in the relevant blockchain addresses.
The fact that millions of users are carrying out this type of audit - albeit informally - every second of every day on almost every address (implicitly) in the blockchain is why public blockchain cryptocurrencies can be unbacked. It is public consensus integrity that underwrites public consensus value and it isn't substitutable by any 'math'.
Privacy ConsiderationsThe challenge for cryptos therefore, is to support privacy demands
against this background. Thats the difficult part.
Of course you can create privacy by obscuring something. The clothes in someone's wardrobe are totally 'colour-fungible' as long as the wardrobe stays closed. But w.t.f. is the point of colour in the first place then ? It's an emperor's clothes scenario.
Thats why obscured blockchains are ten a penny - they are "off the shelf" software that barely require any developers which is why they sprouted up like mushrooms after a rainshower last year. But who cares when it isn't money anymore. It just takes one rogue wallet to be mass marketed and confidence is up the spout and value down the drain. What use is "math" when nobody can tell (using the most basic of century old techniques described above) what's going on on the blockchain.
Nor is 'public consensus' the only reason why public blockchains are fundamental to engendering value, there are down to earth practical ones as well. Dispute resolution in commerce (not using 'viewkeys' because the payee doesn't want to give me it), partial record keeping (such as the income/expenditure side without the balance sheet side which is common in about a zillion business), and simple promotion of financial integrity to name but three.