In MSIE (on Windows), interactions between scripts and applets takes place by means of ActiveX. Microsoft prefers to treat applets as a special kind of ActiveX object. Netscape shows a similar preference towards treating applets as Java components.
If you are developing web based applications for a captive audience who you know will be running MSIE on Windows, then this technology may be appropriate for your project.
However, ActiveX is not supported on Netscape and, in fact, is unlikely to be well supported on any other browsers aside from MSIE.
Coupling this with the fact that it is not supported outside the Windows platform, you will almost certainly find Java to be a more portable solution. The Java solution is also secured better than ActiveX, which can expose the internals of your system in ways you would rather avoid.
For a high degree of Windows integration and a very Microsoft oriented solution, ActiveX is ideal. For portability across platforms and browsers, it's likely you'll do much better to select Java.