Mistwell
Crusty Old Meatwad
Very favourably, because of the ability to impose disadvantage and absorb a bunch of damage. The barbarian will have a lot more HP: 285!!! But the dragon will be doing a lot more damage, and the barbarian will be doing less...I think? If the barbarian does reckless attacks and brutal strike their DPS goes up but their survivability goes down. I'll let someone else figure out that math.
Without doing reckless attacks, our naked barbarian has a DPR of 26. Meanwhile, the dragon's DPR becomes 38. So the barbarian survives a bit longer, 8 rounds, but only does 208 damage.
Realistically, the monk should be able to solo that dragon with just a bit of gear; it's a heavier lift for the barbarian. Also, this isn't just for 1v1 fights; once damage resistance kicks in I think it likely that the monk, current 2024 version, is the best single-class tank in the game in most situations at levels 18-20. That doesn't feel right.
Maybe something like a paladin with a barbarian dip is tougher? Paladin 17, barbarian 1, fighter 2?
Edit: spaced out and was thinking the barbarian's AC was strength and con, not dex and con. That dragon is doing WAY more damage.
I seem to recall an analysis of the new Barbarian doing the most damage in the game and nearly that much damage in a single round at those levels?