Zerocash offers far stronger and more complete privacy than anything I'm aware of.
Reusing an old comment about Cryptonote (which is what monero uses IIRC). Similar analysis applies to Dash, which I believe uses some (no doubt "improved") version of CoinJoin. :
All anonymity is not created equal: you're better off if we can only figure out that one out of 6 billion people bought a Nickelback album, then if we know it was either you or one guy in Tristan da Cunha. The size of your anonymity set matters and Cryptonote provides a rather small one in comparison to Zerocash. This is not to say Cryptonote is worthless, there are tradeoffs between the two, but Zerocash has a distinct advantage in terms of anonymity and I think it matters.
Cryptonote's ring signatures scale linearly in the number of people your transactions are mixed with. As a result, you can't mix an individual transaction with that many people without it getting too big and too computationally costly(chaining transactions doesn't solve this). In contrast, Zerocash mixes every transaction with every other transaction ever[1].
If you are worried about maintaining privacy given repeated interactions with merchants or others who already have some partial information about you, the size of the anonymity set matters considerably. Longterm intersectional attacks are a major problem with anonymity systems. The smaller the set you mix with on any given transaction, the easier it is for some third party to use outside information to eliminate everyone else in the mixing set (e.g because she knows no one else in the set was online at the time of the transaction or was in your approximate geographic area), and determine the true spender. One of the few effective defenses we have for this is to simply include as many people as possible in the anonymity set. If you want to avoid companies building financial profiles of users from the blockchain, this is precisely the type of attack you need to thwart.
[1] Technically, up to 2^64 transactions and the networks ability to handle the spent serial number list. So there is a limit, but it's rather large.
I can't do an apples-apples comparison to the ones you listed because I'm only familiar with Bitcoin and the original Zerocash paper. I can say that the zkSNARK approach to crypto-currency is certainly novel and they have a great team of competent cryptographers and engineers on the team.
That is to say, Zcash isn't a hobbyist effort, it's the result of serious crypto engineering. It's not clown-shoes privacy.
No, I'm not making an appeal to authority. Sorry if it sounded like that.
The team behind Zcash has serious technical chops, and it's worth pointing out that some of the most competent cryptographers and engineers in the world are working on this project.
They've openly published the paper behind their protocol and their code base is open source. They aren't going the "trust us, we're kind of a big deal" route.
If you don't want to bother to understand (e.g. if you don't consider yourself a subset of "really smart people"), then you have to find some other metric to decide whether or not to trust it. I offered the backgrounds and reputations of the people involved as one possible heuristic, but feel free to choose another if you prefer.
Well the question really is, how do the masses start to use this? If only couple of smart people understand it, it won't help much. There are already lot of "like bitcoin, but anonymous" coins, which haven't gained that significant success. If most of the people can't understand why this one is "the shit", they aren't going to see difference between this and the other privacy-promoting altcoins.
