GApps is basically Google's version of a productivity suite online and Live Workspace is Microsoft's version. (You should look them up, this is going to be a very rough post).
Both Google and Microsoft offer e-mail, word processing, spreadsheets, presentation slides and websites, as productivity and collaboration tools (packaged differently of course).
Google has some great extras. Postini is one of the industry's leading security and archival solutions. Everything in GApps runs in your browser. You can install Google Gears and GApps can run offline in your browser. GApps also has API access (paid version) plus thousands of applications written on Google App Engine can be thrown in. The Salesforce CRM tied up with Google too.
Workspace uses Office for editing. I think it's an 'ok' assumption since most people do use MS Office. What's good about that is your formatting is preserved. Google's formatting is pretty barebones.
Overall GApps has more features while MS who has a stronghold on the offline market is moving online. Google rules the online space but it will be interesting to see what Microsoft does.
Google still has a few things to iron out. It goes crazy sometimes when too many people are editing one file. The calendar refuses to save stuff sometimes. My mouse gestures in Gmail stopped working randomly. But those are all small issues.
Microsoft is really working on the usability of their new Live suite. It sounds promising. I tried the new MSN but I didn't like it, only because it's damn slow. The Photo Gallery uploads straight to Facebook and handles tagging as well, that's pretty cool I thought. And they're supporting Mac as well now. Nice of them.
Google is hitting the enterprise market online while the enterprise giant Microsoft is just starting to get online. Lets see how this turns out!