1/2 The privacy on PIVX is implemented as a Zerocoin protocol. That said, you can destroy a specific denomination (e.g. 1 coin) and then mint the same amount as a new coin.
I can 2nd that. In PIVX you "burn" a coin. That gives you a cryptographic "ticket". You then keep the "ticket" as long as you want, then hand in the "ticket" for a new minted coin.
The newly minted coin then has no history. It's so simple and elegant. PIVX didn't invent this, but they've successfully implemented this in the code, and that says a lot.
PIVX's PoS system allows for greater decentralization and equitable block reward distribution. PoS is also not vulnerable to 51% attacks. https://blockonomi.com/51-attack-calculator/