In IE, I can use the classid "clsid:CAFEEFAC-0015-0000-0011-ABCDEFFEDCBA" to tell it to use java version 1.5.0_11. Is there an equivalent for Firefox and other browsers?
I can use the classid "clsid:CAFEEFAC-0015-0000-0011-ABCDEFFEDCBA" to tell it to use java version 1.5.0_11
Not any more, you can't, for good (security) reasons. See http://java.sun.com/javase/6/webnotes/deploy/deployment-policy.html
There is an IE-only clsid mechanism for asking for "5.0_(something)" in general - http://java.sun.com/javase/6/webnotes/family-clsid.html . This was introduced in 5.0u7 so if you have any one JRE from u7 onwards installed you get this behaviour, otherwise you get the old and incompatible behaviour.
Sun did not deign to provide a similar mechanism for other browsers until 6.0u10, when they added a bunch more mechanisms for choosing versions and deprecated all the old ones including the 5.0u7 family chooser. See https://jdk6.dev.java.net/plugin2/version-selection/ for all the gory details.
So what behaviour you get depends not only on the browser and whether the version of the JVM you want is installed, but what other versions are installed as well. The new behaviour is at least consistent, but it is completely different to all that went before and not entirely compatible. By the time your apps' deployment HTML has been updated to cope with it, they'll probably work with 1.6 anyway.
So in summary, as usual with applets, the whole thing's a bloody mess. Yay.