Some numbers for perspective. Assuming 50% base chance to hit, 18 strength, advantage, a greatsword, and 18-20 crit range using relentless attack on a critical hit. I don't know if the extended crit range of the weapon also increases chance to hit or damage. If that is the case, the damage would increase a bit. At this level a maximum of 2 extra attacks can be generated by Relentless Attack, assuming the first two attacks crit.
[0.25 * 0] + [0.4725 * (7+4)] + 0.2775 * {[0.25 * (7+4)*2] + [0.4725 * (7+4)*3] + [0.2775 * [0.25 * (7+4)*4 + 0.4725 * (7+4)*5 + 0.25 * (7+4)*6]]} = 15.17 damage.
On 4 attacks, this is a round output of 60.68 damage. This does cost the barbarian some resources in the form of maneuvers, but even after those are used up the resourceless dpr (assuming advantage can be maintained) comes to 30.34.
The illustrious Lightning Bolt in deals 8d6, which averages 28 damage, halved on a succesful Dex save. Assuming 50% chance to deal full damage again. Per target this comes to an average of 21 damage.
This means a full turn of hitting things with the Berserker is comparable to attacking 3 targets with the Lightning Bolt spell.
A wizard has 2 of these a day, 3 with arcane recovery. The Berserker has 3 of these full-attack turns per short rest. Of course, a wizard has lower level spell slots as well, and the safety of range, and the Berserker needs to be in melee with 2 targets for this to work, but even without 2 targets and exertion points the Berserker deals about 30 dpr. This all assumes advantage, I don't know how easy that is for the Berserker to keep up, because I don't know your campaign. I will let people draw their own conclusions on the powerlevel.
If I missed something, let me know.