I can't clearly compare with Monero since I don't know it very well but I can explain a bit how blackbytes work.
You can see blackbytes as bank notes which have their transactions history writted on them. You can see this transaction history only if you own them, there is no public ledger. That's mean that if you receive a payment in Blackbytes, your payer can't know what you will do next with the blackbytes he sent to you. He could know that only if the same blackbytes return in their hands which will become very unlikely if Byteball network becomes bigger. You can still protect yourself against this possibility by using a wallet dedicated to privacy, at start you just need to get some bytes anonymously to fund the Blackbytes transaction. If someone would discover the history of a blackbyte you used, it couldn't link it to anything since he can't see your other transactions made with blackbytes.
In overall there is no way for anybody to get a picture of what's going on with blackbytes, all the transactions are kept private by every blackbyte user. If you want to try to find a flaw, you simply can't, cause you can't get the data. 
The novel system blackbytes use is an excellent compromise between privacy, transaction time and fees.
If I would need ultra-privacy, I would simply hide behind a monero and a blackbyte transaction to get the best of two.