It's just like normal programs, such as Microsoft Word. Java servlets run inside a web server. Servlets are actually really fast, and can be more efficient than CGI scripts. Much of the cause for speed concerns is actually over applet loading - large applets take a long time to load initially. Thankfully, Java applications and servlets are not subject to such slow loading times.
Applets are inherently unreliable.
The differences between Netscape and Internet Explorer make it impossible to write stable applets. These differences can be frustrating for developers and users. There are often workarounds though, and applets should always be tested with a variety of browsers. The optimal solution is to use a single JVM, which will be used across all browsers. Sun Microsystems, the creators of Java, have come up with the Java Plug-in.