It's hard to be enthusiastic about this packet when the major flaws of the previous weren't addressed at all. We are given Barbarian and what it does is point out, even more dramatically, what is cause for concern: Barbarian is just another step in the Martial Dominance direction.
Let's look at an average human barbarian at a few points along the way:
Stats: STR - 18 (15+2+1), CON - 16 (15+1), DEX - 14(13+1), WIS - 12(11+1), INT - 10 (9+1), CHA - 9 (8+1)
Attack Roll: +5 (+4 +1) plus Reckless Attack (Get ADV, grant ADV) plus Rage (Get ADV, no reactions)
Damage: 1d12+4 (MDD: +1d6) (Rage: +2)
AC: 15, HPs: 15, Resist: Bludgeon, Piercing, Slashing (in Rage)
On average, the barbarian will be hitting probably 70% (or 91%) of the time for 14* damage. Toss in Rage, and the hit sits at 91% and the damage goes up to 16* per. (*not counting critical hits). A limited use Magic Missile (2d4+4 for 9) that doesn't miss will not average as much damage as the average attack of a barbarian, much less a raging barbarian. Since Rage will basically last an entire encounter, even at first level, they'll be hitting 91% for 16 each through many attacks possibly. Half damage from every normal source will mean that the Barbarian's 15 HPs essentially doubles in that time.
By level 5, it'll be:
Attack: +6 with ADV
AC: 15, HPs: 55, Resist: B/P/S (3x/day), 70% chance to avoid death blow
Advantage on Init
+10 to Movement Speed
Picking up an improvised chair leg, a level 5 Barbarian could go into a rage and have advantage on attacks doing 1d3+3d6+8 damage.
Keep in mind I didn't even bother with Feats which would improve the class even more. But that holds true for every class.
Yes, the Barbarian is a very cool class. In fact, it'll expect to see quite a few requests in my playtest campaigns to use one. I suppose the only way to playtest it, though, is to compare it's relative power and enjoyability against the other Martial Classes because the spellcasting classes simply are far behind in comparison.
In fact, I could make a DEX based Barbarian as a ranged/finesse attacker.
DEX: 18, CON: 16... whatever on the rest.
Ranged Attack: +5, Damage: 1d8+1d6+4 (ADV with Reckless)
Melee: +5 (finesse), 1d8+1d6+4 (+2 rage) (ADV only with Reckless)
Dual Melee: +3/+3 (finesse), 1d8+4/1d6+0 (+1d6) (+2/+2 in rage) (ADV with Reckless)
AC: 18/17 (DEX+CON+TWD in melee), HPs: 15 (Resist: P/S/B in Rage)
Not bad. Reckless from range wouldn't be all that bad (range would allow fewer return strikes), so those longbow shots at advantage would tear through a lot. Two-Weapon Defense boosts that Dual Wielding format to an AC of 18, couple that with 15 HPs, and they are better defensively than the Fighter in melee. Still better at range, really, because AC 17 and 15 HPs is an improvement.
Or maybe they pick up Rapid Shot and use Reckless for two attacks with advantage doing 1d8+4 each while Reckless.
At any rate, compared to the limited use Wizard, the Ranged Barbarian would still be a much more dangerous foe. A couple of times a day of 1d4+2 (x2) attacks versus non-stop use of 1d8+4 (x2) that probably hits 91% of the time. Even single target, 2d4+4 (100%) isn't better than 1d8+1d6+4 (91%). Disadvantage you say? AC 17 being attacked at Disadvantage vs +5 Attack gets hit about 70%. The Wizard gets hit 30% (AC 15, with Mage Armor). Pretty significant, yes, but the Wizard probably had 8 HPs, the Barbarian has 15 and will be taking half damage in any two battles they feel threatened in. My money would be on the barbarian surviving better. If the Barbarian plays it safe (no Reckless), they hit 70% for 1d8+1d6+4 which is still better, on average, than two no-miss magic missile - a limited resource.
Anyway, Barbarian looks very cool... but in the greater picture, I can't really give any true account of how it plays because I see Martial Classes as all being too good at the moment.