RMI is well named - Remote Method Invocation. It allows Java-to-Java remote method calls. A nice thing for sure.
SOAP is badly named. It is not simple, not object oriented, not an access method and arguably not a protocol. But it is highly interoperable. You can provide SOAP services or call SOAP services using just about any language, OS, platform, etc. I call it the lowest common denominator. Common because so many diverse platforms can use it, but low because XML involves a lot of expensive
string handling for composition and parsing, XML is a fat payload, HTTP is not your fastest protocol choice (of course SOAP can be done over others, but HTTP is most common). I think the common makes the low worth while when you value interoperability.
Hope that helps you compare the two
