Cryptocurrency Privacy: Evolving... Zerocash (ZEC, ZCL, ZEN) vs All Other Coin

[George Violaris]

On 01/10/2017 7:42 AM, grarpamp wrote:
> Rethreading these two former threads into a more General: Item...
> 1: Zerocash: Addressing Bitcoin's Privacy Problem GoogleTechTalks
> 2: Why I can't sleep soundly with blockchain, being the cypherpunk
>
> ##########
>
> https://zcoin.io/zcoins-privacy-technology-compares-competition/
>
>> Blockchain privacy is a particularly difficult thing to achieve as a public blockchain is designed so that all transactions are transparent and the supply of coins can be publicly verified. Privacy mechanisms have to ensure that these elements are preserved so it’s a conflicting mix of protecting privacy while maintaining public verifiability.
I'm trying to understand what kind of crypto algorithm is being used in 
Zcoin. Is it any similar to cryptonote/bytecoin's ring signatures and 
such? I understand that transmitted coins are burnt and new ones replace 
them, but IMO this doesn't cover privacy fully - it's mostly the way the 
transactions/coins are transmitted that matters, is it not?

In short my question is, how does zero knowledge proof compare to ring 
signatures employed i.e. by Monero?