If I need a web service to pass back and forth a complex object, is there a reason I should prefer SOAP over REST? Here is an example of the possible SOAP message:
I view SOAP and REST as orthogonal APIs, designed to do different things.
SOAP is basically a fancy RPC, so if you want to send a computation request over to the server and get the result back, you use SOAP. If it would be local, it would be a method call to an object instance.
REST is a way to create, retrieve, update and delete remote objects, not in the sense of POO, using a uniform API. If it would be local, it would be like working with a file.
So they actually respond to different needs. You can bastardize one to do the work of the other, but you mangle the meanings.
Your first requirement of "passing back and forth a complex object" constrains your architecture to eliminate many of the benefits of REST. SOAP is designed for accessing remote objects, REST is not. REST supports passing media-types as simple as text/plain, which is far more primitive than dealing with an object.
If you haven't seen it already, this question and its answers cover most of the REST vs SOAP issues.
If you develop both the service and the client, using SOAP is as easy as REST (actually easier).
You may prefer SOAP over REST if these conditions meet:
The entire service API is complex, not just one object.
The service is used within a relatively small network, and performance is not an important requirement.
You decide to spend the minimum amount of time to develop both the service and the API documentation.
One major benefit of REST is that all you need to call and use it is a browser and a HTTP stack - pretty much every device and machine has that. So if ease of use and reach are you main goal - use REST.
One of the major benefits of SOAP is that you have a WSDL service description and you can pretty much discover the service automatically, and generate a useable client proxy from that service description (generate the service calls, the necessary data types for the methods and so forth).
So if discoverability and a strict, formal service description are more important to you, use SOAP (with the downside that you need a full-fledged SOAP client to call your service - your web browser won't be sufficient).
SOAP isn't harder to use - but it's just not quite as "pervasive" in terms of being available - any browser can call a REST service and get an answer - but then it needs to parse and interpret that response. SOAP gets nice data structure, but you need a SOAP client for this.