Quote from TransmorpherDDS >>

I agree... we can have a discussion about this without devolving into petty insults for the people we disagree with.

As for the point that more things should cause exhaustion... I can see how that could be a way to balance out Berserker and make it feel like less of a trap than it often does, but the simple fact remains that, unless I'm mistaken, no other subclass in the game has an ability that induces exhaustion. If it was a more common mechanic it wouldn't feel so punishing to have a subclass whose primary ability causes it. Are you in a game where Exhaustion is a regular concern outside of your Berserker abilities? Well, then you might as well not have a subclass, because if you're trudging through the desert and getting exhaustion from heat stroke every day, then you just can't frenzy. Meanwhile, literally every other Barbarian Subclass can do everything you do, plus some other thing, even if it's something stupid like being able to wear spikey armor and hug people to death.

 Honestly there are so many ways this could be tweaked. Give them a way to gain exhaustion recovery on a short rest. Give them free x amount of frenzies a day. Make it a con save or take exhaustion. have them recover multiple exhaustions on a long rest. I am not against there being a cost or risk to using frenzy but it cannot be so crippling people don't use the ability for sessions at a time. Or scrap the whole frenzy thing and give it a damage boosting ability. Perhaps removing its own damage resistance to inflict vulnerability to damage the barb does. really lean into the whole berserkers do not care if they hurt themselves to get the job done. 

Our group has a Berserker Barb and while he isn't using the Frenzy much due to the cost, the Mindless Rage bit has been of use a number of times.  In a recent encounter, our foes were charming us and 2/4 fell unconscious in the fight.  We were left with....Barbarian and Monk, both of whom don't much fear charms.  Pretty easy fight from there, with the biggest threat now a non-threat.

It's obviously a situational answer.  If your campaign is likely to have a fair bit of mind controlling attempts, then maybe the Berserker is a better option.  Otherwise, pick what flavor you prefer for your story and enjoy it. From a mechanical standpoint, it is obvious that different situations will lean more toward one or the other.  Unless you know with some certainty what you'll be facing, it's a gamble either way.

To the surprise of probably no one, the Zealot is the way to go.

If you're not careful the Berserker can be a trap. Frenzy can literally kill your character. If you want a bonus action attack, take Polearm Master. Mindless Rage is nice, but Intimidating Presence is not. Want to frighten people? Be a Conquest Paladin. Retaliation is OK.

The Zealot has several nice features. Divine Fury gives a nice early dmg boost with scaling, and there is no cost to activate it. Warrior of the Gods is ok, not great. Fanatical Focus is a nice option which can be potentially life saving. Zealous Presence is nice, even though you don't get to use it very often. Rage Beyond Death is awesome, and a great Barb capstone. It synergizes terrifically with Persistent Rage which can make you potentially unkillable while raging for up to 5 minutes.

The problem with the whole Barbarian class is a general lack of great features after level 5, but the Zealot is one of the most fun options for the Barb.

Zealot, because Berserker's main feature causes exhaustion.  At higher levels, gives you the ability to ignore fatal blows, which is both mechanically amazing and flavorfully awesome.  Warrior of The Gods can be really powerful if you have a cleric that can cast revivify or raise dead, as they can essentially cast it indefinitely.  That way, your barabarian can possibly "sacrifice" itself, only to be revived by a trusty cleric during the next rest.