Is it beneficial to Hunker Down when I'm at full cover already?

Usually when I hunker down behind a bit of half-cover, the cover indicator goes 100% solid, as if I'd been behind a better bit of cover. It also gets a little outline and an "up" arrow above it.

However, the cover indicator is the same if I hunker down behind a piece of full cover. Is there any further benefit from hunkering down behind full cover? Or is it just a waste of a move?

Hunkering behind full cover works as advertised.

On the PC version of the game you can go back and left click on a unit after its move is complete, click the ? icon (or F1), and see his stats. I did a quick test on a support in full cover and his defense went from 40 to 80.

Also don't forget hunkering also gives immunity to critical hits... sometimes by itself that's not a waste of a move.

Yes - it is benefical. The 'full shield' just represents 40% cover.

Hunker down 'doubles' your cover bonus. So if you've got half cover (20%), and you hunker down, this becomes 'full cover' and thus you get 40%. This is why you get the 'full shield'.

If you hunker down on full cover (40%), it goes to a massive 80% cover, and if you include some smoke or ghost armor - you'll pretty much be close to untouchable...

You can also see this effect with the sniper ability, where it treats half cover as full cover. The shield will switch from 'half' to 'full'.