Some of Squaretrade's warranties cover physical damage, which AppleCare doesn't.
Last time I checked, Squaretrade's warranties are only worth the initial replacement cost of the device. If you buy a $1500 Mac, your Squaretrade warranty is only good for $1500 worth of repairs. So if the screen goes out during year #2, costs $800 to get replaced, your Squaretrade warranty will only cover $700 worth of repairs after that.
AppleCare doesn't have that dollar limit. If your screen goes out 5x in year #2, it doesn't decrease the amount of coverage at all.