Based on
this article and my limited experience with
Java Help there seems to be several major differences. The first and perhaps most significant is that Eclipse Help actually runs off an embedded
Tomcat server. My recollection is that Java Help merely finds the HTML file on disk and displays it. With Eclipse Help you would be able to use JSPs and probably other technologies since it runs off of Tomcat. As far as I'm aware that's not possible in Java Help. Also, the article mentions easily converting Eclipse Help to standalone documentation. That might be possible with Java Help too so I can't say whether or not it's a difference. Also, because Eclipse Help runs off of Tomcat you can take advantage of the Apache Lucene search engine. I'm not aware of what engine Java Help uses or how they compare.
Overall, it sounds like Eclipse Help brings more overhead and a little complexity with a lot of added flexibility. Of course
you should research this on your own and make your own decisions, that's just what jumped out of me and may be inaccurate.