Earlier I used to believe in Java, a bit more exactly Java to Micro Environment (J2ME). This technology was dedicated to be the bridge between the different mobile platforms (Symbian, Palm, Linux, Windows mobile, etc). How? There is (or at least should be) a so calls Java Virtual Machine (JVM) for all the operating systems (OS) to enable the J2ME applications run. So the architecture is simple: You have a device with a specific OS, with the proper JVM installed. Then You can take any J2ME application, and run it on your device, just like the applications specific to the OS of your device. This is a common interest of both the provider of the OS and Java to create and distribute JVMs and let as many user have it as possible. It is rather promising to see the developing power that creates J2ME applications, and many of them for free!
I could still believe in it, if I had no bad experiences with the different JVMs. For example, the JVM for Palm OS simply does not support bluetooth (the JSR-72 API is missing), though a lot of Palm devices are equipped with bluetooth radio. Once the JVMs are not providing the same environment, J2ME applications cannot be absolutely universal anymore.
And, once a PDA browser is generally able to handle the web applications, we have got the universal solution that is independent from operating systems. There is no use to develop applications for the different operating systems (the same product for J2ME, Symbian, Palm, Win Mobile, etc.) so that as many users can use it as possible. Internet access is a MUST for each PDA maker, so there will most likely be no PDA without a web browser.
So, probably the PDAs of the future will have the following mission: a robust OS with a full-featured web browser