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From the data I have obtained, I have concluded that Protection 3 will protect you as well as Protection 4 will with only very insignificant differences in damage taken over a long period of time--much longer than a PvP fight.
Observations: In addition, Protection 4 seems to have used more armor durability (I didn't test too much on this). When dealt 2 hearts of damage with a Sharp V sword upon a Protection 4 chest plate, the chest plate lost 2 units in durability; whereas, a Protection 3 chest plate, when dealt 2.5 hearts of damage, lost 2 units in durability.

Of course, this is the average of the results because due to Minecraft's range of damage inflicted upon a single strike, health damage received will vary (equally).
Furthermore, it costs more experience to repair a Protection 4 chestplate than it does to repair a Protection 3 chestplate of equal durability.

The experiment design consisted of 2 testing zones for each chestplate: "Damage from an arrow shot from a dispenser" test, and "Zombie with Sharp V sword" test. Each test zone consisted of 2 individual tests that were repeated due to the varying ranges of damage that can be dealt. Tests consisted of the "Health Damage received" test and the "Armor Damage received in proportion to Health Damage received" test.