Too many things to quote...
First, let me say thanks to [MENTION=6852869]Lillika[/MENTION] for some excellent analysis. Those are exactly the sorts of thoughts I was originally looking for.
I've done some more math where I dropped feats entirely and compared Wolf Totem with Berserker. Since the exact number and damage output of a Wolf Totem's allies can vary a lot, I went with an estimate that is, I believe, on the conservative side of average. I assumed that he has 1.5 allies in melee each using a d8 weapon and gaining an Extra Attack at level 5. I assumed an average 65% chance to hit (which, if my advantage math comes out right, means an expected additional 35% damage). I also took into account Retaliation (which I didn't before). However, since Retaliation only comes in at higher levels, I also included a chart that gives values for before 14th level.

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("All Frenzies" means if we theoretically just dropped the exhaustion penalty entirely.)
Things that weren't taken into account include critical hits (this won't matter much for the barbarians, since they all get advantage, but it might slightly increase the wolf's damage), and all of the other variables that can't be anticipated. Every campaign is different--this is just baseline math.
Before I comment on the chart, I want to briefly address some of the other points that were brought up.
There has been a suggestion that we compare the Berserker's 6th-level feature to the Totem Warrior's 3rd-level feature rather than the same level feature. If we do so, we can assume that the Bear Totem's feature is more or less equivalent to the Mindless Rage. It is highly campaign dependent. In most campaigns, you are going to have plenty of both types of effects. (As far as the Bear Totem not having his feature up when he needs it, from 7th level on he can avoid surprise, so that isn't, in my opinion, an extremely weighty consideration.) So let's say those are roughly equal in effect. If we have to make a decision, I'll let us say Berserker is a bit better off.
That leaves us comparing a Berserker's: Frenzy, Intimidating Presence, and Retaliation, with the Totem Warrior's: Spirit Seeker, Aspect of the Beast, Spirit Walker, and Totemic Attunement. Retaliation is really good, but Totemic Attunement is pretty nice also. Let's, again, be generous to the Berserker and say it gets the edge, even though I'm not sure that's true. Aspect of the Beast and Intimidating Presence are pretty close in my opinion. If anything, Aspect of the Beast gets the edge here. So that leaves us with Frenzy vs. Spirit Seeker and Spirit Walker. Spirit Speaker and Spirit Walker are utility, but put all together are pretty nice. The Totem Warrior can do effective scouting and other information gathering. This is contrasted to Frenzy, the benefit of which is a hotly contested thing.
If we assume that Frenzy is intended to be used about 1/day (aiming for your last fight) as a situationally useful trick, then you can probably say the subclasses are more or less balanced taken over all 20 levels.
All of that is assuming a comparison with
Bear Totem. If, on the other hand, we make a comparison with
Wolf Totem, damage gets more complicated and depends not just on party composition, but on number of times frenzied.
As you can see, in order to keep up with Wolf Totem before level 14th, we need to be frenzying about 3/day. After that, we can drop it to 2/day. This is problematic for a couple of reasons.
Once your Berserker is Frenzying multiple times per day, the mechanical benefit of the feature drops in effectiveness, as the exhaustion counteracts some of the benefit through reduced initiative and mobility (as well as non-combat utility). If Berserker vs. Wolf Totem frenzies only 1/day, his damage is pitiful compared to the damage contribution of the Wolf Totem. At that point it is straight up Wolf Totem: Damage, Berserker: Immunity to charmed and frightened. (Well, not exactly. Totem Warrior also gets significantly more utility).
So again, we end up with the 1-20 balance being within reasonable toleration, as long as the Berserker only frenzies 1/day.
That leaves us with problems.
The first is that Berserker isn't functioning as advertised. When you look at the theme of the Berserker path class, what do you think it
should be best at? What is supposed to be its shtick compared to the Totem Warrior? Before reading the mechanics, I absolutely would think, "damage output." This is the guy that says, "I'm the BIG weapon--hit them with me!" Looking at the mechanics, the first thing I see is "Frenzy." Cool! I can make extra attacks, which is such a big deal that I get worn out afterwards. Yep, this guy is the damage king.
But that isn't what we have. We have a guy who can be immune to charmed and frightened. That appears to be his actual stick. For damage, pick a Wolf Totem Warrior, or take a feat. Berserker can get a tiny bit more damage with the same feats, but not enough to be worth taking the class for, compared to what you could get with the same feat and a Totem Warrior of your choice. And if you do stick with that safe 1/day frenzy, you aren't even getting much out of that subclass until 6th level. You've got 3 levels of Totem envy to wade through before you get that immunity to charmed and frightened.
And perhaps even more important (depending on what matters more to you) is that using the Berserker's ability for more than the final fight (hope you guessed right!) makes him fall right out of his niche. I'm the barbarian,
I should be the one kickin' in the doors, bending the bars, and lifting the damn gates! But, nope. Not after frenzying. Now the guy with a Strength of 12-14 is the better choice for the group's muscle. And if I'm trying to go for even more frenzies, I might be slowing down the whole group today. I'm also going to suck tomorrow. Instead of being the mighty raging warrior, after actually
using the features that look like I should be using them, I become the guy slowing everyone down and not doing my job in exploration. That bother me just as much as the first one.
Here is my conclusion on what they intended in design:
You were supposed to frenzy 3/day, and the drawbacks weren't supposed to be a big deal.
If that were the case, then Berserker would function as advertised. Sure, Wolf Totem can contribute more damage if it has enough helpers, but you get to do a lot of
personal damage, which is what you are (supposed to be) all about. Unfortunately, as I explained above, the rules do not support wielding your Berserker in such a manner.
Fixing it by dropping exhaustion entirely is actually perfectly balanced up to 13th level. After that, it seems to me to make the Berserker way too strong. So that still leaves me wondering about an elegant way to balance damage.