ROA (REST Oriented Architecture) is just a fancy name for a SOA (Service Based Architecture) using REST services.
The main advantage of SOAP-based SOA over ROA is the more mature tool support; however, this could change over time. Another SOA advantages include the type-safety of XML requests (for responses, ROA can also use XML if the developers desire it).
The main advantage of ROA is ease of implementation, agility of the design, and the lightweight approach to things. In a way, SOA and SOAP is for people in business suits; that's what you'll find used in the banking and finance industries. Conversely, somebody that needs something up-and-running quickly, with good performance and low overhead, is often better off using REST and ROA.
For example, when explaining why they chose REST over SOAP, Yahoo! people write that they "believe REST has a lower barrier to entry, is easier to use than SOAP, and is entirely sufficient for [Yahoo's] services" (Yahoo! Developer Network FAQ, as of February 2008). This is true not only of REST vs. SOAP but also of ROA vs. SOA in general.
Another advantage of REST lies with performance: with better cache support, lightweight requests and responses, and easier response parsing, REST allows for nimbler clients and servers, and reduces network traffic, too.
As REST matures, expect it to become better understood and more popular even in more conservative industries.
A few words on hype vs. reality. In the comments below, I've linked to Pete Lacey's excellent criticism of SOAP, "The S Stands for Simple". And here's another one, by Alex Bell, published in Communications of the ACM (vol. 51, no. 10, October '08): "DOA with SOA".