While the Abjuration Wizard is impressively tanky too, he cannot halven the damae twice before it is even considered.
I mean... Nothing stops you from multi-classing Rogue to get the exact same tools as your Barbarian build to do that exact thing.
Not that you need it, since you can reduce everything to 0 easily enough anyway (If it even hits you because Shield reactions)
Barbarian is an easy tank, because you can get a bunch of resistances level 3 with Bear Heart - Which can combo with stuff like Stallion or a popular choice is going Moon Druid to get Bear (And later Owlbear) form while Raging for extra health from the form plus all the resistances from Rage.
But Abjuration Wizard with Heavy Armour Mastery is the best tank, due to having the best mitigation (Especially if you hoard up magical items that grant uses of Abjuration spells for free Ward charges), especially when using Warding Bond to provide the resistances. Taking literally 0 damage from almost everything. It's just a little trickier because it doesn't come online properly until after Grymforge as Adamantine Plate is the first available heavy armour with damage reduction.
Not that such min-maxed things are necessary in the game, especially when you can have characters fully devoted to dealing damage that still are pretty tanky due to high AC's and utility spells (Shield, Counterspell, Darkness etc)