Some currencies such as Monero and Zcash focus on protecting user privacy as much as possible. What information is available from the blockchains of these currencies?
Number of wallets? Transaction details? Anything else?
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Unlike many users might think, Bitcoin blockchain is completely transparent linking all your transaction history and those who you are transacting with. Everyone who has ever transacted with you or will be in future is able to see what amount you have received from or sent to which address, forever. Some (centralised) mixer/tumbling services try to mitigate this fact changing your BTC into some completely other ones, but they still have their history and you don't know what it is.
Privacy focussed coins try to solve this at protocol level, I'll try to summarise:
Dash (and Pivx fork) offer you an option to use a sort of CoinJoin which is performed by their Master Nodes and can have several rounds. This is pretty similar to tumbling services but you are not at risk to loose your funds. However, you still have to wait for mixing partners in every round you make and this can take minutes up to several hours for every single round. Since the amount of mixing partners is very limited, an attacker could simply offer high supply to mix with and be able to track your mixed funds anyway.
Verge is a joke. It's basically Dogecoin over TOR hiding your IP but having a completely transparent blockchain. Their Wraith protocol just uses some other notation for receivers addresses, but they are stored in plain on the blockchain.
In Zcash, Zcoin you have an option to use ZK-Snarks and send your transparent funds to a shielded z-address. Unfortunately ZK-Snarks are very computation heavy and need several minutes on modern hardware computers for each transaction to be generated, they are not available for mobile devices yet at all. They are fully shielded hiding sender, receiver and amount of a transaction. However, they are barely used and no exchange or payment service is accepting them to date, so you have to claim them back on their completely transparent t-address blockchain before being able to spend them.
Monero (beside some small forks of it) is the only coin with mandatory privacy enabled for every single transaction. Ring signatures obfuscate the real sender, stealth addresses hide the receiver and (ring) confidential transactions hide the amount of the transaction by default. Unlike all the optional private coins you cannot tell how many Monero wallets are in existence nor how much has been transacted. An external observer cannot say who send how much money to whom. Even as receiver you still don't know the sender's address, you can only determine it by your sub-address or payment id used.
From my knowledge Monero is the most "private". It obfuscates the number of coins held on every account on the blockchain (you wont find a Monero richlist), but most important, it obfuscates in every transaction by default: the sender, the receiver and the amount.
One of the flaws in Monero is that it doesnt obfuscate the ip adress by default but someone using TOR or i2p would still manage to do this. But monero team will implement this in the future with the Kovri release.
I dont like Zcash because there is a 20% block reward for the creators of the coin built in its blockchain, seems not much decentralized, but I dont know much about its tecnology, just that it has a richlist so for me it doesnt work (if someone knows my adress therefore knows how many coins I hold).
Verge: This coin obfuscates just the ip adress of the user, the information is pretty much linkable. And its a fork of Dogecoin '-'
Dash: Not much of a privacy coin, the majority of users dont use the privacy option so if you are one of the few using it someone can link you to a transaction.
Pivx: Hadnt studied much about that one, but has a richlist...