Generally speaking, devices such as headsets, keyboards, mice and external media devices all work fine on both operating systems. Since both Ubuntu and Chrome OS use the Linux kernel, this makes sense. Unfortunately, this doesn't mean that what works on one platform is going to work the same way on another.
For example, Bluetooth devices, USB headsets and webcams have the same level of compatibility across the board and generally work easily without any configuration. Printing and scanning, however, tend to be spotty on Chrome OS while working easily on Ubuntu.
Ubuntu advantages and disadvantages: There are very few USB devices that won't work out of the box on Ubuntu. Brand name webcams, storage devices, printers and other miscellaneous peripherals work flawlessly on the Ubuntu desktop. Ubuntu detects most printers with zero setup and scanners can be used with SimpleScan software.
Chrome OS advantages and disadvantages: Chrome OS offers the same great USB device support as Ubuntu. Webcams, USB headsets, and other related peripherals all work just fine right out of the box. As for wireless devices, Chrome OS is installed on "built for Chrome" hardware which ensures that wireless also works.
On the downside, cloud printing and scanning are horrid on Chrome OS. If you want to scan something under Chrome OS, you need a Web-based scanning interface or an app like CloudScan. As for printing, you'll need a new CloudPrint-compatible printer. If you want to use a legacy printer, you'll have to print from another PC.
I've given it a lot of thought and after much deliberation, I've come to this final conclusion: Ubuntu destroys Chrome OS.
Now, I'm not saying that the Chromebooks running Chrome OS aren't interesting. They do offer great functionality for the basic browser-based tasks. But if you ever plan to print or scan anything, you will need to make sure your peripherals are compatible.
In my honest opinion, unless you've never used a computer before or want a "kid's toy," you'll want to use Ubuntu over Chrome OS.
Think I'm wrong? Do a Web search for "Install Ubuntu on Chromebook." You'll notice a plethora of articles catering to Chrome OS users installing Ubuntu onto their Chromebooks. There's a reason for this. Chrome OS is painfully limited despite the added functionality made available in the Chrome Web Store.
Ubuntu mirrors Chrome OS by offering a software repository from which to download new titles. The difference is, you can run Ubuntu software without being connected to the Internet.
Am I being too harsh? Perhaps I am to a degree. I think Chrome OS is a great portable OS option, but it's hardly a replacement for a full operating system experience.