I tested the berserker against my fighter excel sheet, and the berserker deals more damage than the fighter everywhere except levels 11, 12, and 13 if you assume 1 frenzy per day, 6 encounters per day, and Retaliation each round. Heck, I'm beginning to like the idea of moving Retaliation to the Barbarian proper as a level 11 ability, as it would be functionally equivalent with a fighter's 3rd attack.
Are you factoring in abilities like
Action Surge and archetype specific abilities? If so, the Fighter who can manage to net himself advantage in key opportunities is capable of doing far more damage than a comparably built Barbarian in all but the most extended of encounters (without factoring the Fighter's capacity to utilize their own reaction, which would send them through the roof).
Now, that's not saying I don't like yours. I went and reread it, and the only thing I'm worried about is the level 14 ability. Taken with everything else, it's another big boost to power. As it stands now, as I said in another thread, both barbarian paths' level 10 abilities aren't really combat abilities, they're utility and defensive abilities. You moved the level 14 ability to level 10, and then added another attack at level 14. So your berserker has, effectively, 4 attacks per round at level 14, when the fighter has to wait till 20th level.
Do note that
Retaliate has an activation requirement of suffering damage from a creature in range, in addition to using up the reaction. Fighter (and Barbarian as well, lowering the value of Retaliation) can also easily gain access to the reliable use of a reaction attack through feats like
Sentinal,
Mage Slayer, and
Polearm Mastery feats without necessitating the loss of HP, and usually being more versatile in their utilization. For the sake of comparison, at level 20 a Fighter should have no trouble getting 6 (5 at 11) attacks a turn without using
Action Surge or
Haste.
While
Retaliate may be a combat ability, so was the old
Intimidating Presence. And moving
Retaliate to level 10, despite being a signature combat ability, was done because I feel it creates a much more sensible progression in combat capabilities. Frenzy without exhaustion is simply too much raw power, regardless of its actual overall value, to balance at level 3, and still straddles that point from 6 on (and besides, Mindless Rage is actually in a really good spot, it doesn't need to move), up until higher levels. Giving it before level 11 would be far too much. And since Retaliation itself is only about on par with the minor points of some other feats (indeed, many Berserkers might still have interest in taking the above mentioned OoA feats), putting it at level 10 is the safest option for the ability.
While Wizards themselves does state that caution should be taken when giving combat abilities to the Barbarian archetypes at level 10, they don't even follow their own advice with their Berserker or Battlerager archetypes anyway. That said, I would not be adverse to giving my Better Berserker something more fluff oriented in addition at level 10 (and for this, I'm completely open for suggestions), I just don't see a problem with
Retaliation itself where I have it.
Reckless attack while raging isn't a penalty in my book, as the resistance to damage makes up for getting hit more.
If you already have advantage, which I maintain is not particularly difficult to get in 5e as a melee fighter, especially if you're using the expanded combat rules from the DMG,
Reckless Attack typically becomes redundant, only serving to increase the damage you take. Having it act as a requirement for use fits with the "all in" concept of the Berserker, giving players a reason to consider the use of the ability even in situations where it would normally present exclusively downsides. And while resistance definitely does help in this situation, it's mostly there to balance the fact that a Barbarian is going to be giving advantage to his enemies most of the time anyway.