The main thing of it is that Armored Defense grants LAR which acts against every attack that meets it so long as it is in place as opposed to a non-Armored Defense power which only uses whatever sets it has which then go poof until next time it is used (or next round if it has a duration). It's basically a specific cheapo version of interference, some of the penalties of which are mitigated by taking Hardened Armor (it probably warrants mentioning that while not specifically prohibited the wording of Armored Defense and Hardened Armor seems to suggest that the latter is not supposed to be taken with HAR-granting powers. YMMV).
Alright, bear with me a moment I cooked up a couple of examples to demonstrate the functional differences. We've got two heroes with similar defensive powers:
'Crunch' is a harried accountant by day and a budding telekinetic hero by night with Subconscious Deflection 2HD (Defends. Extras & Flaws: Always On -1, Permanent +4) as his primary means of defense.
'Slither' on the other hand is just a lizardman trying to make it in a non-lizardman's world, he has Scaly Hide 2HD (Defends. Extras & Flaws: Always On -1, Armored Defense -2, Hardened Armor +2, Permanent +4). This gives him 2 points of Hardened LAR.
Example 1:
In two alternate universes our heroes have chanced upon a crack den and being eager to thwart villany are looting the place, only to be interrupted by Crackhead McGee coming back from picking up his grandmother's prescription at the Rite-Aid. He attacks them in both universes with a sawn-off 12-gauge shotgun, rolling 2x8.
Crunch's Universe - Crunch's automatic 2x10 precedes McGee's 2x8 in the initiative order, scattering the shot. While McGee is standing there dumbfounded Crunch force-shoves his attacker out of a window.
Slither's Universe – McGee's 2x8 computes to 3 shock and killing to the torso (shotgun damage is WSK+1), Slither's 2 Hardened LAR changes the shock damage to 1 and mitigates 2 of the killing damage into shock. The damage total is now 3 shock and 1 killing to the torso. If McGee's shotgun somehow had penetration the result would be the same. Wounded, Slither hisses and pounces across the room to give McGee a vicious hiding.
Example A:
McGee is back for revenge! Having just got out of traction he has gathered three of his buddies and ambushes the heroes, bursting into a Taco Bell bathroom stall to set upon them with iron bars (club damage is WS+1). They roll 3x6, 2x10, 2x2 and nothing.
Crunch's Universe – Crunch yelps as the first blow (3x6) comes down on his outstretched right hand badly spraining it with 4 shock damage. Worse, having suffered an injury he takes a gobble dice to his highest set (the 2x10 of his Subconscious Deflection), the pain robbing him of his protection when he needs it the most. Even if this weren't the case his defensive ability would only be enough to block one of the remaining blows. He is then struck in the head and right leg for 2 shock each and proceeds to suffer an ignominious and smelly beating.
Slither's Universe – Slither grunts under the staccato impact of iron on his scaly hide, taking only 1 shock to the head, torso and right leg thanks to his ophidian resilience. If the third of his attackers had instead wielded a particularly sharp switchblade (WS+1K, Pen 2) the damage to his right leg would have only been 2 shock (shock reduced to 1, 1 killing mitigated to shock) thanks to his hardened armor. Met with a roar the attackers recoil as much from Slither's sudden ferocity as the now apparent roiling stench and are set upon with verve and frenzy.