I know that you can improve performance and battery life by not having Flash on your Mac. Is there any similar advantage to not installing Java?
Installing java won't have much effect on battery life.
I don't think installing Flash will have much effect either.
Where the issue is is when you hit a website with badly written flash (and to a very much less extent Java) where the animation takes up CPU but you can just leave these sites - you will be no worse off than not installing.
Java is now rare on websites and not really used for parts of the web site the user does not need.
I think a better way is to install a plugin for your browser like ClickToFlash which stops Flash loading until you tell it.
Yes - you won't have to worry about updating software that Apple seems to be less and less inclined to let run. It also has earned a reputation as software that you want to devote time and attention to patching or making sure you never run code you don't trust.
If you're not going to block java in the web and take measures to secure it, you'd be better off not installing java on OS X from a security and maintenance standpoint.
Personally, I decline to instal flash and disable java entirely on my portable Mac so that I have less running, better battery life and less security exposure and reduced maintenance.
By not installing java or flash, you have two less things to update and two less things to run content while browsing the web.