I have been reading through and also noticing this. I was looking for a better explanation too - from what I understand basically:
Monero uses ringCT algorithm on transfer to mix the payments and obfuscate the sender
Monero has a private view key and separate spend key. View key can decrypt transactions made by you to confirm your total balance (Monero balance is unknown to daemon, is calculated as (xmrRecieved - xmrSpent)
ZCash has 'zero-knowledge' proofs and while the whitepaper[1] is a bit intense it uses a novel Proof-of-Work explained within. Called zero-knowledge Succinct Non-interactive ARguments of Knowledge (zk-SNARKS).
ZCash coins origins obfuscated before recieved by user, reducing need to mix payments together
Personally, I think they're both great and it's a healthy time for a privacy-based cryptocurrency face off. Having said that, ZCash theoretically sounds better (to me) yet Monero is proven in the wild - and both have people with money already sunken in.
IMO the cryptocurrency world will be much better off when it's userbase is looking for a CURRENCY and not a COMMODITY.
[1]: http://zerocash-project.org/paper
[2]: https://github.com/zcash/zips/blob/master/protocol/protocol....
[3]: https://www.reddit.com/r/Monero/comments/41vg68/monero_vs_zc... - decent ZEC vs XMR ELI5 thread
edit: formatting