I tried both these great programs on my desktop and here is some of my analysis
Both program are equally effective in indexing and can index all types of microsoft office files, pdf, text, mp3 and pictures.
Personally, I found the interface of Copernic better and easy to navigate.
Filehand give you results in google type format and you get lot of options per document while in the result window itself
The Preview pane of Copernic wins by a great margin and the way it groups the results is quite intelligent.
There are rumours that even Google is coming up with such a desktop search application. So we can expect some great wars for this market in the near future.