Claim Human task via API or expose it via WS ...

If I understand your question correctly, it is recommended to always use as much OOTB features as possible. I would advice using WS where possible instead of building custom code using API's. The alternate option is to create a plug-in smart service that uses the API to expose the functionality as required. This is more of a managed way of using API's

I use forum forum.appian.com/.../5436
ryan.gates WS , but I have deployed it , but it is lack of documentation
I need some help on how to use it . It is axis based WS providing reports capability on appian processes and workflows