Web services (which can be SOAP or REST based), you may call them also APIs, have little to do with RSS feeds (from my point of view).
Web services generally will provide an interface and exchange data. How they are implemented behind the interface they expose, it's not relevant to the client.
Wikipedia defines web services as a "software system designed to support interoperable machine-to-machine interaction over a network." As implementation they are more complex than RSS feeds and are usually used to integrate business applications (like connecting an ERP with a CRM system).
On the RSS part, all decent CMS should have RSS available (in a form or another) generally for sharing content.
From my knowledge Joomla! don't have any web services implementation (Joomla! is working on a draft document as we speak). Wordpress has XML-RPC Support.
So it's kind of important to understand what does "data" mean. Do you strictly refer to content (like articles, blog posts) or do you want to exchange other data as well (for example user data or other data stored in the CMS tables).
So to kind of answer your question, to integrate articles from all CMS probably using RSS feeds will be enough.