Links to both the packages are here
Which of these packages is better to use and why?
I'm the author of both, so I can help clarify this: they're actually different versions of the same package!
wordpress-rest-api is the older version, we renamed it to wpapi for consistency and brevity prior to our 1.0 release. If you install wordpress-rest-api you should get a deprecation notice instructing you to use wpapi instead.
wpapi will be used going forward for all future releases.