Better Suited for Mobile Development than RIAs
JavaFX Script was first designed with the mobile market in mind. In this context, I think it has a good chance of success because of its rich graphics and agile development features. In addition, the Java runtime is already installed on millions of phones without any performance issues.
In the actual RIA space, however, JavaFX Script is basically a wrapper around Java2D and Swing and as such the only RIA solution it offers is within a browser applet. As we all know, applets have been pretty much dead, mostly due to deployment and startup/performance issues. JavaFX Script applets in their current state would have no chance at all against their smaller Flash-based competitors or Microsoft's Silverlight (which can solve the deployment issues by just forcing all Windows users to download it via Update Center).
Fortunately, Sun seems to be well aware of these shortcomings. They are tackling this issue in a variety of ways. First of all, the Consumer Java Runtime Environment (JRE) project (due as an update to Java 6 in the second half of 2007) is supposed to modularize the JRE and reduce its download size to around 2MB with additional modules downloaded on demand. This means among other things that a small fix in some minor library will not force you to download the entire JRE but rather just that small module. The Consumer JRE project also plans to reduce the startup time of Java applications, including applets. I greatly recommend you read Chet Haase's blog on the subject to get an update on how a consumer JRE should revolutionize the Java user experience.
Sun Has Some Work to Do
However, until that project actually sees the light of day, Java applets (be they Swing or JavaFX Script) have little chance of success against Flash or Silverlight in the RIA space. The mobile market, however, is a huge opportunity for JavaFX Script, as the Java platform has a great lead over any other competing technology. JavaFX Script should help make that lead even greater, provided Sun delivers the world-class development tools it requires.