---cost
assuming that it takes 2.5 seconds per sword-hit (since knockback on the sword and other effects can throw the players quite some distance), and that diamond armor has on average around 469 durability, it takes 19.5 minutes to wear down a set of diamond armor.
for iron armor, i'll assume that it takes 1.5 seconds per sword-hit. iron armor, with 213 durability, takes 5.3 minutes to wear down.
so although diamond is more rare and expensive versus iron, it lasts longer, which might nearly make up for the difference.
---damage done
another benefit is that diamond and enchantment allows for potions:
damage to diamond armor prot iv from damage II potion: 0.5
damage to diamodn armor prot iv from diamond sword sharpness v: 0.5
damage to diamodn armor from damage II potion: 1-1.5
damage to diamond armor from diamond sword : 0.5-1
damage to iron armor from damage II potion: 2.5
damage to iron armor from iron sword: 1.5
as progressively weaker items are used, mroe damage is done, but diamond armor prevents potions from becoming op
---battle length
with iron armor, sword, and damage potions, a battle might last only 10 seconds (6 seconds to land 4 sword hits and 4 seconds to throw two potions), and the defeated has trudge back from where he came. assuming that takes 30 seconds, 25% of time is used for whacking at each other.
with diamond armor and enchants , a battle would last up 40 seconds (40 seconds to land 20 sword hits). again, assuming the two parties meet every 30 seconds, more than half the battle is spent... battling.