Many websites are set to detect when they are being viewed on a mobile phone, and they change the layout to make it more 'mobile-friendly'
That is to say, the site takes up the full width of the screen, there are fewer wordy menues and so on.
The full desktop site has a different layout, because there is more screen space on a regular desktop computer.
it detects whether to serve the desktop site or the mobile site based on the operating system
if it's Winf=dows or OSX, then it wil sere the desktop version.
If it is iOS or Android, it serves the phone version.
Your Android tablet has a lot of screen real estate, so it wil probably look a bit better with the desktop site.
But it is your own decision as to which version to use.
Good luck :)