The defense rating on your gear doesn't matter unless your in iron banner. The toughness stat in your subclass loadout determines how much health you have , usually making a difference of about 15hp. It does matter crucible since it lets you survive getting one shot my tripmines and getting 2 shot by hawkmoon and timurs lash (without luck).

At max, it gives about ten extra HP. I am referring to class stats. Armor rating is meaningless in PvP

The defense rating of your gear is normalized, but subclass stats armor, recovery and agility do matter.

Armor (the bar on your skills page) how much hp is in your health bar. Defense (the number on your character screen) is damage mitigation. The higher it is, the less damage you take. I am unclear how this comes in to play in pvp when the level advantages are disabled. In pve, if you are at a disadvantage level-wise relative to an enemy then the effectiveness of your defense and attack is reduced accordingly. In pvp with advantages disabled, I would intuit that this would not actually impact the defense value so a person would with a higher defense value would have more damage mitigation than a player with a lower value. But this is not the case given that it normally takes the same amount of damage output to kill a 32 as it does a 5. So I am thinking that the advantage being off in pvp doesn't merely eliminate the reduction in effectiveness that is present in pve when there is a higher level enemy; rather, it just baselines everyone attack/defense-wise. Tl;dr: "armor" makes a slight difference in pvp because it amounts to bring your hp. Defense doesn't make a noticable difference in pvp unless level advantages are enabled.

In the Crucible no, but Iron Banner yes.