You cannot afford good heavy armor at level 1 though
Yes, you can. Both Fighters and Paladins start with chainmail in 5.5e. That's the third-best ordinary heavy armor in the game.
and the best you can afford provides the same AC as medium armor with a +2 dex modifier
Barbarians do not start with any armor, not even medium. The best heavy armor Fighters can afford is, as stated, chainmail which provides 16 AC. If the Barbarian sacrifices a bunch of their starting gold for it (two thirds of it, in fact!), they can get scale, which only gives the 16 AC, meaning the Barbarian is still behind (even with a shield!) because of fighting style.
, or no armor with a 16 con and 16 dex. You're not getting Splint Mail at level 1. So Chain and Shield is 18. And Scale + Dex + Shield is 18, and Unarmored Defense with 16 Con and 16 Dex and Shield is 18.
Why would any Barbarian do this? They cannot use Dex for weapons. Sure, finesse weapons
exist, but they're incompatible with Rage. "When you make an attack
using Strength—with either a weapon or an Unarmed Strike" etc., emphasis added. (Believe me, I'd LOVE it if Rage worked with Dex, because then I might be able to sell a DM on allowing the Zealot subclass to function as a 4e Avenger, which would be a significant thing for me.)
The best either is doing is 18, unless Fighter is choosing Defense for their Fighting Style.
Why would any Fighter
specifically trying to be durable at 1st level NOT do this? They can switch out as soon as they hit level 2, so they aren't even locked into it.
So, no, I don't accept that there are a bunch of 1st level Barbarians going for 16 Dex and 16 Con.
One of those two stats--most likely Dexterity--is going to be only 14 at best, which means you aren't getting more than 15 AC via Unarmored Defense. Fighting Style is not needed, but isn't a cost either, as noted. Any 16 Dex/16 Con Barbarian is stuck being less accurate and doing less damage while Raging until they get to a much higher level (4 minimum).
Also, note that of the three,
only Fighter gets a Fighting Style at this level (and Barb never does!), so Defensive puts the Fighter that much ahead even over the Paladin.
1st level Fighter can do 16/14/16 for Str/Dex/Con, meaning they sacrifice no long-term potential while still having the best AC a 1st-level character can get. Chainmail (16 AC), sword and board (+2 AC), Defensive style (+1 AC), and anywhere between 2 and 5 uses of Second Wind per day, typically 3-4.
So yeah, I stand by what I said. The only way the Barbarian can be even
debatably "more durable" is if they sacrifice their long-term potential for a tiny AC boost that still won't get them up to par with the Defensive Fighter.