Dan Boneh, Henry Corrigan-Gibbs, and Stuart Schechter have proposed Balloon Hashing: A Memory-Hard Function Providing Provable Protection Against Sequential Attacks (in proceedings of AsiaCrypt 2016). Taking the abstract at face value, it is a blow (pun intended) to Argon2, the winner of the (first) password hashing competition, in particular as Balloon hashing boasts
the first practical cryptographic hash function that:
(i) has proven memory-hardness properties in the random-oracle model,
(ii) uses a password-independent access pattern, and
(iii) meets or exceeds the performance of the best heuristically secure password-hashing algorithms.
and further claims
a practical attack against Argon2i that successfully evaluates the function with less space than was previously claimed possible
Is Balloon hashing, or any of the contenders with properties (i) and (ii), ready for practical use (possibly including some Argon2 variant)? With what parametrization (underlying hash, etc..)?
Can we roughly guestimate the security improvement (at equal computing effort, for some definition of that) compared to competitors like the still very ubiquitous PBKDF2-HMAC-SHAx? Bcrypt, which has some traction in servers? Scrypt, which better leverages multiple CPUs and ample memory, but does not exhibit property (ii) and is seldom used?
Note: After Luis Casillas's comment, I have expanded the scope of this question beyond Balloon Hashing.