First off, I'm going to completely ignore the actual in-game stats of the armors. Not only would I say they are rather misleading compared to the designs of the armors(at least when putting similar quality armor up against one another), but they are also primarily used to determine some sort of path for equipment advancement. Instead I intend to look at the actual design of the armors. And on that note...
... I'm also going to overlook the widespread use of bare arms that inexpliably permiates the Nordic and Imperial armor designs. It seems to me that this was likely a result of 1) the developers wanting to showcase the new arm designs, since in Skyrim we can choose how big and muscled arms we have, or 2) the armors were originally designed to allow for clothing underneath, but this feature wasn't implemented, yet the armor design stayed the same. Since both the Imperials and Nords have armor designs in previous games that do not show that much skin, I'm assuming both races would mostly use that.
For the Nordic Hold armors, we have a few things of note. With the exception of Haafingar, all the Hold Guards use Fur Gloves and Fur Boots (or just the boots, for whatever reason, in Whiterun. I'm guessing oversight), all Hold Guards uses the same full helm and there are two main designs for how the body armor is constructed. Both types use chainmail shirts, but one design uses a gambeson and the other uses scale armor. Eastmarch/Stormcloak, Hjaalmarch, the Pale and the Reach uses gambeson, while Haafingar, Whiterun, Falkreath, the Rift and Winterhld uses scale.
On a side note here, it seems odd that they wear the gambeson on the outside of the armor. I think this is another stylistic choice, more than anything, to let the player see the armor combination. This is also a problem with the Imperial Studded Armor.
Now, are these armors good? I would say mostly yes.
Something that is important to note is that a lot of "historically accurate tests" of chainmail armor are not historically accurate at all and, often, don't even construct the parameters of the test correctly. Taking a subpar piece of chainmail (explaining that one in a bit) and putting it against something hard and immobile does not produce accurate results as for how effective these armors were. You need something to simulate the reaction from a human body to being attacked in such a fashion to begin with. Second point is that you need to test it with gambeson underneath, because that is how it was used, which also improves it quite a bit.
The most problematic flaw in many of these tests is that they don't construct proper chainmail, but a subpar version. Now, I'm no expert, so I don't know of any professional terms for these different types of chainmail, but the layman names for the main types seem to be "butted" and "riveted". Butted chainmail would be http://www.darkknightarmoury.com/images/Large%20Butted%20Chainmail.jpg waste of metal, time and effort, where about 2/3 of the rings have a significant structural flaw; it isn't a full ring. This makes it very weak, since most of the armor have a structural defect, and makes it weak to piercing by arrows, spears and such.
Riveted chainmail, on the other hand, would be https://cdn.instructables.com/FH7/U3TY/G5W7CR2T/FH7U3TYG5W7CR2T.RECT2100.jpg; what the metal, time and effort of the butted version should've gone into making in the first place. In this type of chainmail, the structural problem is solved by riveting the rings, making it far, far stronger. Now, these pictures themselves are not meant to be historical examples or anything, just a general idea of how the rings in each style look like. For historical riveted chainmail, it could look something like https://s-media-cache-ak0.pinimg.com/736x/60/84/81/608481bdbac5cfd07b39837e45d8c339.jpg, though i think there were several styles.
Main point, "proper" chainmail was much better than a lot of "historically accurate tests" show. So if you see a test, keep these things in mind.
Another point is that, if it was that bad, it wouldn't be used. If it doesn't save your life against a modeicum of piercing power, the elite warriors would get the smiths to make something better. Yet the chainmail remained in use for a long time.
Gambesons (often called "padded armor" in many RPGs like Pillars of Eternity) is also usually misrepresented. While nowhere near as good as chainmail, it is a decent armor that could stop some types of arrows and cuts and thrusts. And, of course, scaled armor is another layer of metal armor, though that would probably be rather heavy to wear.
In short? The Hold Guards and Stormcloaks in Skyrim would be pretty well protected. Not good equipment compared to the standard issue plate armors of the Legion in the 3rd Era, but, then again, the Legion armor by the time of Skyrim also wouldn't compare to that either. So let's look at the Legion armors.
Getting one thing out of the way right away; the heavy Imperial armor that seemingly is reserved for officers of the Legion is the best armor in use by soldiers we see during the civil war questline. But it is also rather rare and only one non-officer is seen wearing it (Hadvar if you sided with him in the intro) unless the player (who can wear whatever they like during the questline) also uses one. From this, I think it is reasonable to conclude that the Imperial Light Armor and Studded Armor are the most common armors in use in the Legion in 4E201. So how does those compare?
The Imperial Light Armor would be the least defensive armor in use during this civil war. It is leather and could charitably be compared to gambeson in usefulness, meaning it would be outclassed significantly by the armor worn by all Hold Guards and Stormcloaks. And since the Jarls and Stormcloaks can keep their soldiers with proper chainmail, I'm going to be charitable to the Legion and assume the studded armor is the "default" Legionnaire armor. Otherwise, I don't see how they'd not be massacred when engaging the Stormcloaks, given the profound advantage chainmail would give them. Especially since the Legion mostly uses one-handed swords, which are strongly disfavored against metal armor. So I'm taking Belrand's word for it mainly being armor for scouts.
Imperial Studded Armor looks like Imperial Light Armor with a bit of chainmail added around the shoulder and neck areas, which would barely make it more useful than regular Imperial Light Armor. As such, I'm going to work off the assumption that there is a chainmail shirt underneath the leather. And, as such, you could expect it to perform very similarly to the chainmail/gambeson combination used by Hold Guards and Stormcloaks, though probably worse than the chainmail/scaled combination.
In the end? The Haafingar Guards would be the best outfitted among the guards, because their chainmail/scale combination, steel bracers and boots. Most Legionnaires compare pretty much one for one with Stormcloaks in terms of equipment and Legion officers are the best protected soldiers in the war.