But the defenses are not perfectly equal. I’m particularly worried about the barbarian taking hits before he gets to go or running out of rages in a 4+ encounter 1 short rest adventuring day.
I did my own analysis. Barbarians have half the gold fighters do to buy starting equipment. That's a fact. A fighter starts with chainmail and a shield for 18 AC before anything else. There's no reason for a fighter to start with a lower AC.
The second a barbarian makes the choice to add more rations and a decent ranged weapon they've purchased themselves out of that 18 AC for 1st level.
There is no reason for a 1st level Barbarian build for durability to have less than an 18 AC. They can do that on point buy without spending any gold on armor (S16 D16 C16 I8 W8 CH8) plus a shield.
Also what "decent ranged weapon" are you going to buy for a fighter who is using Chainmail and a Shield?
I still think a Chainlock destroys either of these though. 16 Dex, hiding with Armor of Agathys and a Shield spell in your back pocket while your Skeleton, or your Quasit or Sphinx of Wonder with 20+ hps engages the enemy .... and when they die you just summon a new one.
A 4 encounter day is going to put you at 2nd or possibly 3rd level, and if it doesn't they were weak encounters. So I don't think this is a significant concern for a 1st level PC.
Strangely the Goliath Stone Endurance ability works better for Fighters than Barbarians. While raging the damage reduction from stones endurance occurs before resistance's half damage reduction, essentially making stone's endurance half as effective for the raging Barbarian.I guess I am saying it is a more fair comparison for--
human fighter: tough + magic initiate vs stoliath barb: tough + stone's endurance... missed initiative = no problem, use a reaction for 1d12+CON dmg whisked away... do it again, same amount of uses as 2nd wind.
Or dwarfbarb: tough + dwarf-tough. Stack even more HP for the rage reduction to mean even more.
If it is a maximizing comparison you can't then assume the barbarian would minimize durability feat selections to not equalize the magic initiate choice somewhat.
Requires level 2.Warlock does have 1 particularly tanky build. Fiendish Vigor Invocation.