I've been using Google's Desktop Search (GDS) since they introduced it on 14 October. For the past few months I've also been using Copernic Desktop Search (CDS).

I have compared the major differences I noticed between the two below (yellow is a point for CDS, blue=GDS):

• File extensions - I frequently jot things down in the program treepad, which uses the unusual file extension .hjt. With CDS I can set it up to index those without problems - GDS has a very small amount of extensions it indexes, with no configurability except enabling/disabling the few it does support.
• Auto caching - This is where I get most use from GDS - it duplicates your IE history into its own cache, so even if you clear your temp Internet files, the old pages you visited will still be searchable.CDS makes an index of the files in your IE history, but does not back them up itself.
• Result listings & convenience of use - There is no need to keep entering queries and pressing enter while searching in CDS because of the search-as-you-type feature. There is also no limit to the amount of results in the list. GDS is limited to a very small 10 results per page.
• Music, video & images - No options within GDS for these at all, except if the filename happens to be exactly what you search for. CDS is excellent for image and music searching, image searches display in thumbnail view, while the music search goes inside mp3 id tags.
• Obtrusiveness - One of my instant turnoffs with software is it starting up with the system. Marginally worse than that is adding an icon to the taskbar. GDS does both of these, and what's worse does not provide an option to disable either. CDS does include a taskbar icon when it's running, but does not require a system startup.
• Full text indexing of IE history - This is a big advantage Google has, with CDS you can only search the title and file name. GDS indexes the full text.
• Bulk-indexing - CDS is very configurable in this way with lots of different options to suit everyones needs. GDS insists on a very inconvenient hours-long initial index.
• Time to index new files - From my own tests, after the initial time-consuming indexing of your drive, files appear to be added instantly to Google's index; Copernic is slightly slower everytime I've tested.
• Email indexing - I only use web based email and have not had a chance to properly test this, but from what I've read GDS is hands down on this; CDS allows you to search your email, but GDS provides convenience tools like being able to reply & compose emails straight from the results pages. it also allows you to group your emails in the familiar conversation view made famous in Gmail. (GDS does not support searching your Gmail messages yet)
• Presentation of results - GDS shows full text snippets, CDS only has file names. GDS also displays thumbnail images beside history results.
• Firefox support - neither support Firefox yet, though both say they are considering it for the future. A workaround I've been using that works very well is to install the Slogger extension - this converts the browsing history into html files (indexed by both programs by default).

They both score on five of the criteria above, but because Copernic is more configurable and full featured generally, that would be my recommendation instead of Google Desktop. Also worth noting is that Google Desktop is in beta and they will add more features as time goes by.

More info:

·Copernic Desktop
·Copernic Desktop v1.1- Improvements & tweaks list (released on 13 October)
·Google Desktop
·Google Your Desktop - Detailed intro to Google Desktop
·Google Desktop - Vote For A Feature
·Robs Blog - Copernic Desktop Search
·Slogger Extension - Make your Firefox history searchable
·MSN: Desktop Search before Year End
·Yahoo Readies Desktop Search Tools