To begin with, I want to thank the Reddit user "UGAebo" for pointing out why I was wrong about the upper body multiplier affix. As a special thanks to him and you fellow DMZers (whether you are a loot globin like me, some sort of Rambo like others etc), I spent some serious cash and took it upon myself to thoroughly (I hope LOL) test the FMJ affix. Why the RAAL? It is my weapon of choice in all 3 ranked game modes so might as well treat myself with one that has said affix, right? Right?! Well, it missing the FMJ perk and therefore missing its signature 100% wallbang damage so eh, I'll use the upper body multiplier one or the +30% mag capacity and -10% body multiplier and maybe someday I'll spend hundreds of millions until I get one with proper attachment slots and the +1 armor level +upper body multiplier affix combo to absolutely delete anyone who comes my way (yes, if you can, go for that affix combo on main gun is and you'll obliterate anyone). Until then, eh, it is time to grind back I spent on what seemed like 200 something or 300 something RAALs.
Anyway, straight to the point:
I have good and bad news about the FMJ affix.
The good:
It does work like you think it does by making your weapon deal damage as if its rarity was 1 level higher.
The bad:
It doesn't not work like you think it does. It only applies to the chest and stomach. So, whenever you shoot your enemies in the chest or stomach, your weapon's damage will be dealt as if its rarity is 1 level higher.
What does that mean?
A mythic gun will deal bonus damage to mythic armor and even more to anything below, a legendary gun will deal full damage to mythic armor and bonus damage to anything below and so on.
How consistent is the FMJ perk?
I wouldn't call it consistent. The requirement of shooting to the chest or stomach is easy to follow, the problem is that what the enemy does is… well, random. Is the enemy not fighting back (so his chest and stomach are exposed?) Congrats, the affix will trigger the damage bonus. Is the enemy fighting back? Their arms will get in the way therefore preventing you to get the damage bonus, at least to some extent (you also need to factor angle at which you shoot, height, distance, target's movement speed and so on).
Ironically, what I was wrong about the upper body multiplier is what I am right (upon testing) about the FMJ affix. In my opinion, the upper body multiplier is better simply because it is way more consistent + aim assist will help you make it even more consistent by forcing center mass shots, having the advantage of not being affected whether the arms get in the way or not.
Anyway, if you have the chance to, get the upper body multiplier + FMJ affix combo and you'll be unstoppable. If not, just stick to the upper body one.