Hey I use both a Chromebook and a Gen 1 Nexus 7 so I will tell you what I think.
Originally I had just my Nexus 7. I liked it but I needed something to do office work on after my old Windows Vista laptop gave up the ghost. I went with a bluetooth keyboard. The keyboard was nice and there are some excellent office suites available for Android but the screen was just to freaking small. The Samsung 3 chromebook caught my eye as a backup because it was modestly priced at $250. I've been using that since March now. It is a very nice laptop that boots fast, has no noise or heat, and great battery life (around 6 hours on a charge). However, Google Docs apps are not particularly my cup of tea. I don't care for Google Docs Writer (certainly not compared to Office Pro 7). It works offline which is nice but it is sluggish and awkward to work with and you have to thoroughly check formatting since it sometimes munches docs that get opened in other word processors. Chromebooks only support cloud printers as well so if your home office has an old fashioned printer, you'll need an existing Windows or Mac OS machine to use it and have to do a bit of jury-rigging over your home network. A new printer might be a hidden cost for your home office setup here.
Bottom line for me is that while a Nexus 7 is nice and has superior productivity software, the screen is simply to small for prolonged work. I think a full-sized tablet or transformer would do the job much better and leave me happier for office work though those options are of course more expensive. For basic web browsing, streaming, etc. I vastly prefer my chromebook as it has two-button mouse support (android only does one click) and an array of ports for connecting devices that my Nexus 7 simply isn't compatible with. I keep my chromebook docked to a 24'' LED at home and can dual monitor with my external display and the laptop's built-in display. It is very handy for having notes on one screen and my document on the other screen.
TO ANSWER YOUR ORIGINAL QUESTION
Chrome OS is a different operating system from Android. It uses its own app store (Chrome Web Store) and its own apps. So far most of these "apps" are glorified web links to web-based software but there is a small (and growing) collection of offline ("packaged") apps that work like software on other platforms does. So far an office suite more sophisticated than the Google Docs offline mode doesn't exist though.