I'll start with the simplest class feature, which takes inspiration from some of the 4E Primal classes (or at least the tougher, Con based builds). Simply put, if you're not wearing armor you add both your Dex mod AND Con mod to AC. This reinforces the flavor of the "wild" warrior by making being unarmored an attractive option. It's as good a solution as any.
This is the bulk of what the Barbarian does, and there's some good and some bad with its implementation. Not unexpectedly, there's a daily limit but since it starts at 2x/day it's somewhat forgiving. You get Advantage with any use of Strength (attacks, ability checks, and saving throws), which models what's going on really well. The accuracy boost is pretty huge here. You also deal bonus damage, so you're hitting harder, too (as expected). Finally, you gain Resistance to the weapon-based damage types (Piercing, Slashing, Bludgeoning), which at first blush seems awfully potent. I would have expected a
Clearly the benefits of Rage are pretty substantial. When in a Rage the Barbarian is certainly looking like the most dangerous melee combatant in the party, which is as it should be. Without play experience, though, it's really tough to judge whether Rage's drawbacks balance out this awesome power.
Obvious the first "check" on Rage is the daily limit, but there's more to it than that. Your Rage ends when you fall unconscious (tough to do given the defensive buff!), or also if you can't attack for a turn (say, if some enemy restrains you). While this might seem harsh I like the strategic element that it creates. Maybe you shouldn't use Rage if you're fighting a spellcaster that's likely to hamper you enough to waste your Rage. Or if you do, the whole party has its priorities shifted; do everything in your power to prevent the enemies from turning off your Barbarian. Looks like it'd be fun to play!
But Rage also has a final drawback. This one has some major tactical implications - you can't take reactions. While this makes some sense (your fury is extremely focused on just wrecking stuff and you don't have the presence of mind to worry about tactical openings), it also kind of doesn't (aren't you so angry that you'll lash out at anything that moves?). There are also mechanical consequences, the minor one being that offensive output might actually decrease in some situations (since you're not getting in opportunity attacks), but more of a concern is the fact that your stickiness is reduced to exactly zero. It's extremely easy to simply walk away from this raging engine of destruction, and that just doesn't sit well with me. This guy's dangerous. If he has you pinned up against a wall, you should be screwed.
To sum up, I think Rage has a really solid foundation. The main things I would change is to tone down the defensive benefits (DR instead of Resistance), and to compensate for that drop in potency to eliminate the "can't make reactions" drawback. I'm not sure what a good value for that DR would be, though (and perhaps that would have to wait until the math is more finalized). Con mod (but how would it scale)? Equal to Rage Damage Bonus? Con + Rage Damage bonus? These are all pretty simple solutions that result in very different values, so it would really be a matter of looking at the math and picking whichever one "fits" best (a little less than Resistance on average opponents). My gut says Rage Damage Bonus = DR, but without any playtesting that's really just a wild guess.
Another simple class feature that gives you a Rage-like boost (Advantage on your attack) essentially at-will, but with a heavy drawback (YOU grant Advantage). I like it. It's risky, but that's sort of the Barbarian's MO. And it makes you feel like that crazy berserker warrior even when you've run out of Rages for the day.
I remember reading commentary after the first playtest packet with class was released (back in January, I believe) even though I didn't read through that packet myself. The consensus was that the Barbarian was pretty overpowered compared with the Fighter, and most people advocated for powering up the Fighter.
I'm not sure if the balance issue has been fixed or not (this Barbarian does look like it probably has an edge over the Fighter), but at this stage of the game I'm not sure it matters that much. The math can be refined later. What I'm mostly concerned with during the playtest is whether or not the mechanics do a good job of representing the concepts, and whether or not they provide an interesting game experience. Does this feel like a Barbarian, and how would tweaking things affect that? I think mostly yes, it's a good representation of the Barbarian, who is all about the simple application of brute force.