How WordPress hashes passwords

I’m the author of the linked article (thanks for the shout-out, by the way).

The WordPress function that does the hashing is wp_has_password() and, by default, it will run the password through 8 rounds whatever the “best” algorithm the server makes available to PHPass is. WordPress, again by default, uses MD5. However you can also configure things to use Blowfish or DES if you so desire.

For reference, take a look at:

Note the documentation of wp_hash_password itself states:

Creates a hash of a plain text password. Unless the global $wp_hasher is set, the default implementation uses PasswordHash, which adds salt to the password and hashes it with 8 passes of MD5. MD5 is used by default because it’s supported on all platforms. You can configure PasswordHash to use Blowfish or extended DES (if available) instead of MD5 with the $portable_hashes constructor argument or property (see examples).

If you’re still in PHP land, you can port the functionality directly to your new system and have a fair amount of parity with WordPress’ default implementation. You could also just build the new system in such a way that it uses WordPress as the authentication provider (similar to OpenID), then you won’t need to worry about it at all.