What are the advantages a Champion fighter has over a Berserker barbarian?

Question

Both the fighter and barbarian in this comparison are using a two-handed weapon build. I'm asking for the pros a fighter may have in combat over the barbarian because it feels like in combat the barbarian is superior. Things like number of attacks, AC, damage, etc.

What advantages, if any, does a Champion fighter have over a Berserker barbarian?

Evaluation criteria:

1. level 4, no multi-class, point buy, both human, no magic weapon or armor
2. both use greatswords

My initial estimate is that AC for the Fighter is better, while the barbarian has more attacks and more HP.

Answer 1

Berserker is vulnerable to losing their rage

From the description of the rage feature:

Your rage lasts for 1 minute. It ends early if you are knocked unconscious or if your turn ends and you haven’t attacked a hostile creature since your last turn or taken damage since then. You can also end your rage on your turn as a bonus action.

This means that if you don't have a target within javelin range, possibly due to full cover, and haven't taken any damage, your rage ends at the end of your turn. Your DM might rule that you can hit yourself, but that strongly depends on your DM. It also means a disabling status effect, such as that inflicted by hold person or sleep, can mean your rage ends unless you get a party member to help you.

Even if you simply use rage again, it costs a bonus action, so you cannot make a second attack on that turn, and you are also exhausted, meaning you have a disadvantage on ability checks, meaning it's harder to avoid grapples/shoves (though rage's advantage on strength checks means you'll be rolling normally, at least).

Answer 2

Berserker is misleadingly "better" as an attacker, but has other problems

I will start off saying that there are many ways to stat out these two classes and determining the most optimal builds for each class would be overly time consuming and difficult to determine.

Given the following:

Assuming Stats of:
St 18 (Level 4 increase Str by 2)
De 14
Co 14
In 11
Wi 14
Ch 10

Fighter Champion 4

• 37HP (+9.5 effective hp from Second Wind)
• 1 Greatsword Attack at 2d6+4 (great weapon fighting style boosts damage a little)
  • 13.56 average damage, adjusted for crit chance
• Can take two actions once per rest
• Can heal self for 1d10+4 hp once per rest
• Expect to be in splint armor; AC of 17 (Full Plate soon, in theory)
• Crit on 19-20

Barbarian Berserker 4

• 41HP
• 2 Greatsword Attack at 2d6+6
  • 13.65 (27.3 per round) average damage adjusted for crit chance (ever so slightly higher)
• Can give self advantage
• Rage gives resistance to physical Damage
• Expect to be wearing scale; AC of 16
• Exhaustion is a problem

It appears that Berserkers have more HP, resistance, and get double attacks (which is all true), but that doesn't paint the full picture. Not only are you going to be easier to hit with a lower AC (easier still if you attack recklessly), but you're going to be stacking up exhaustion, which you don't have any way to mitigate.

Given your constraint of "only one combat", then the exhaustion doesn't come into play, but if you're berserking more than once per day, you're creeping slowly towards inefficacy and perhaps death, until the cleric can remove the condition.

Additionally, at level 5, the fighter creeps even closer when both classes get Extra Attack; Fighter 2 attacks; Berserker 3 attacks.