A Turing complete script can read and write data on the block chain, so in theory it can do anything a block chain core protocol can do.
An EVM app must obey the rules of the core blockchain protocol; it cannot rewrite them.
I wrote "in theory". If the scripts are not truly Turing complete, then it is possible the core protocol has some limitations which would preclude implementing certain features. Whether or not Z.cash can or can not be implemented in Ethereum's scripting model is unknown since Ethereum has not been finalized.
Just remember, "Ethereum can do anything because it has scripting". 80/20. Remain focused. Buy the dips.