Applets and Flash are different technology. When first introduced, Applets had a lot of security holes in them, you could effectively run your program on the Client side which is not what any customer wants. Later this technology was improved substantially. On the other side Flash is more light weightlightweight than Applets were. People more readily accepted Flash and didn't consider it as a security threat. Apart from minor vulnerabilities that do occur in Flash plugins, Flash was much safe. The initial security setback hurt Applets dearly. Also you are right probably Sun didn't pursue Applets that aggressively.
Something similar to Applets and probab;yprobably more useful, is the native client that Google is trying to build for Chrome. Let's see how it goes.