The direct impact damage from Wither skulls is not reduced by the Projectile Protection enchantment, unlike damage from Ghast/Blaze fireballs. This may be intentional, but it's inconsistent with ghast fireballs at least.

To reproduce

This is most easily reproduced in a world with no nearby mobs and mob spawning disabled.

• Give yourself two leather helmets, leggings and boots; enchant one set with Projectile Protection IV and leave the other unenchanted
• Set a repeating command block that clears the Wither effect from the player
• Set /gamerule naturalRegeneration false and change to Hard difficulty and Survival mode
• Summon a wither with the following command:

   /summon wither ~ ~ ~ {Attributes:[{Name:generic.follow_range,Base:0}]}
  

  • The wither still attacks, but will stay in place and not chase you, making it easier to get away from it.
• Approach the wither and get hit by one of its skulls while wearing the unenchanted armor, heal yourself to full health and repeat the same with the enchanted armor.
• Spawn a ghast and repeat the same.

Notice how the Projectile Protection armor significantly reduces damage from the ghast, but not the wither.

Code analysis

This is likely because in net.minecraft.world.entity.projectile.WitherSkull.onHitEntity(), the damage source passed to the target entity doesn't call setProjectile() (like ghast/blaze fireballs and arrows do).