If fancy client support is really an option it would usually be better to use a zero-knoweldge authentication protocol (like SRP), though one of these KDFs could be used as a preprocessing step.
Can't you do that with any password hashing alg?
There are really two reasons for this: (1) optimization is a really big deal; some impls go so far as to have asm for specific architectures or use architecture-specific features like SSE2 and (2) there really isn't very much code for a cryptographic primitive, typically <=1000 lines. (e.g., see https://github.com/khovratovich/Argon2/tree/master/Argon2i/r...).
Once a simple reference implementation is hand-checked, it can be used to generate comprehensive test vectors for other implementations.
This isn't my area of expertise, but I believe there's some research in applied crypto for implementation verification. I know https://github.com/GaloisInc/cryptol is a language that's supposed to help in that regard, but I don't know offhand who all uses that.
If you can also write an implementation in something such as Haskell, verifying the input/output between the two implementations is a great way to assure it works as expected.
Another reason for C and assembly is that when everything your algorithm manipulates is a bunch of bytes you don't get much advantage from a type system.
I expect there will be a long review period before the winner is considered suitable for common use. It reminds me of the backlash at NIST for some late changes to the SHA-3 winner, Keccak: https://en.wikipedia.org/wiki/SHA-3#NIST_announcement_contro...
Anyway, as best as I could tell, the consensus on the public mailing list was that the best case for a singular winner would be an amalgamation of four finalists: Argon2, Lyra2, Catena, and yescrypt. Each of them has some properties that are desirable. I'm curious to what extent Argon2 will be modified - and especially curious if the final spec will have tunable parameters / multiple modes or be a one-size-fits-all deal.
Edit: If you're interested in more information, a decent starting place is this paper: https://eprint.iacr.org/2014/881.pdf If you folks want more reading material, I can pull some emails from the mailing list