I'm using a Nexus 10 tablet and I was surprised that SE serves me the mobile version of the site by default. The full version is much more useful on a tablet, with exception of chat which has some issues on tablets.
My user agent is 'Mozilla/5.0 (Linux; Android 4.2.1; Nexus 10 Build/JOP40D) AppleWebKit/535.19 (KHTML, like Gecko) Chrome/18.0.1025.166 Safari/535.19'
The official way of distinguishing an Android tablet and a phone is to watch for the "mobile" part in the user agent (https://developers.google.com/chrome/mobile/docs/user-agent). Not every single Android tablet follows this convention, but it seems to be the official guideline from Google.
From the Google Webmaster blog:
Tablets offer a browsing experience that can be as rich as any desktop or laptop machine, in a more mobile, lightweight, and generally more convenient package. This means that, unless you offer tablet-optimized content, users expect to see your desktop site rather than your site’s smartphone site.
For Android-based devices, it’s easy to distinguish between smartphones and tablets using the user-agent string supplied by browsers: Although both Android smartphones and tablets will include the word “Android” in the user-agent string, only the user-agent of smartphones will include the word “Mobile”.
Please change the user agent detection so that tablets following the Google recommendations are recognized properly.
Additional sources for distinguishing Android phones and tablets: