The primary drawback of light armor compared to heavy armor is that it’s not as tough. This perk will do a lot to alleviate the problem (as long as you don’t compare your perked-up light armor to equally perked-up heavy armor). Take it if you wear light armor, end sentence.
Hey, do you wear light armor? Take this. As long as you’re wearing only light armor (and light armor in each armor slot) it’s even better than a rank of Agile Defender. Stacks with that too.
Light armor’s primary advantage over heavy armor is that it weighs less and does a lot less to reduce your movement speed. If for whatever reason that’s not good enough, then Unhindered is something you can pick up. That said, with light armor weighing less than a third as much as heavy armor, you’re unlikely to need the weight savings anywhere near as much. If you really need more carrying capacity badly, you’re almost certain to get a stronger effect out of the Steed Stone. Theoretically if you never invest in your Stamina you might benefit more from Unhindered in that regard, but a light-armor wearer who doesn’t put anything into stamina -and- needs a high carrying capacity is a rare bird indeed.
This, on the other hand, is hugely useful. Stamina recovery is very important in combat, so if you plan on fighting in melee at all or even just running while wearing light armor, you want this perk. Take it, and sprint forever (not really, but half again as much is quite a lot). Even if you’re not interested in Unhindered, this might be a good enough reason to take that perk anyways- especially if you’re a melee combatant and eat stamina with your power attacks.
Oh look, even more armor bonus. Keep in mind that the light armor you wear has to be entirely a matching set, and all of that matching set, in order for you to benefit from the perk. That makes this perk much less useful for people who don’t have the necessary Smithing perks to craft their own light armor, so that’s where the decision on this should stem from. If, on the other hand, you’re lucky enough to make sure you always have a matched set of armor anyways....
A sadly unreliable perk, you really don’t want to count on this one to keep you alive in a close fight. One-in-ten chances are alarmingly fickle, so don’t take this perk thinking it’ll change the outcome of that close battle that you narrowly lost before loading your save. On the other hand, it’s a constant chance so it does still have a noticeable effect, particularly in longer fights where you’re taking a lot of small hits rather than more occasional hefty blows to the face. By all means you want to take this, just... don’t rely on it to save your butt at a critical moment. You can’t control it.