Axis is ridiculously slow, as in minutes instead of milisenconds. If you are planning on using WebServices for anything business transactions, I would use JAX-RPC or SAAJ. These are both much better technologies
From when is the book you have read?
If they recommend JAX-RPC, then the book cannot be too recent. JAX-WS is to be preferred nowadays, if you are to do SOAP web services.
Are they talking about Axis or Axis2?
There are two different versions of Axis, which are quite different. I suggestion you make some tests yourself.