I'm in a survival world and I came across a pirate ship and it had a FP 3 leather cap in the chest but I already have a full set of iron armor. I'm not as well versed in item stats as others so I was wondering which one I should use.
Iron by far. The only time you will likely be on fire is fighting zombies burning in daylight (and will burn for only a couple seconds), fighting Blazes for the first time. Once you do that, any other time you wind up on fire is exceptionally rare and 100% avoidable.
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A leather helmet with Fire Protection III will be better against fire/lava and being on fire but otherwise an iron helmet is better*, and I'd much rather have better protection against all sources and use potions of Fire Resistance or a water bucket to protect me against fire damage (armor only reduces damage, including burn time if enchanted with Fire Protection, while Fire Resistance gives you total immunity and water immediately puts you out, and also helps avoid accidents in the first place; e.g. pour water over lava to turn it into obsidian). Damage from being on fire (not in fire/lava) is also slow enough that you can easily out-regenerate it (unless you are playing on a version prior to 1.9).
*Calculations: a full set of iron armor reduces damage by up to 60%, 52% against lava (4 damage penetrates 2 armor points for -8% damage reduction) while a leather helmet in place of an iron helmet reduces damage by up to 56%, 48% against lava; Fire Protection III reduces fire damage by a further 24% (6 EPF * 4% per EPF) which acts on the damage that got through armor for an overall damage reduction of 60.48% (48% + 52% * 24%) against lava (this is about the same as you'd get with unenchanted iron armor prior to 1.8). You also get a 45% reduction in burn time after leaving fire or lava (15% per level, using the highest level on a single piece); only enchantments reduce the damage from being on fire so you'll get 58.2% (45% + 55% * 24%) less damage overall compared to iron armor (for comparison, you burn for 15 seconds after leaving fire or lava, which will normally take away 15 health, reduced to 6.27 with Fire Protection III on one piece of any type of armor).