Its called Allotek nanohives which all you gals use.

Be honest with your self if range amps were better would you choose them ove dmg mods? No. 30m of range amplification is great for cqc.

Our two combatants will be A with Damage Mods and B with Shield Extenders.

A basic Caldari or Gallente suit has 330 total HP without skills.

The basic AR does 425 dps.

A has 330 HP and does 467 dps
B has 396 HP and does 425 dps

A kills B in 0.84s
B kills A in 0.77s

So, as we seen, the health granted by Shields is a minor boost to survivability. However, damage mods are most effective on Proto weapons, as the percentage yields higher numbers. The base DPS of a Douvale AR is 468.75, with a damage mod its 515.63.

So:

A has 330 HP and does 515.63 dps
B has 396 HP and does 468.75 dps

A kills B in 0.768s
B kills A in 0.705s

In conclusion, the difference is negligible. Shields have a numerical advantage, but the reaction time needed to take advantage of it is pretty much inconsequential. However damage mods on a proto weapon versus a basic weapon makes the difference much closer, and skills in weapon Proficiency and Shield/Armour Upgrades has the possibility of changing these numbers further in favour of Damage Mods.

This only holds true on a 1 to 1 scale as Damage Mods have a stacking penalty. However one can stack 2 Damage Mods with minimal consequences, and if they still have high slots after, decide wether they want the extra 5% damage or an extra 66hp shields.

Yay! Let's make a "CQC king" out of an assault suit. Who needs scouts anyway! Gal medium should be king of everything - wtf not? We should also remove Forge restrictions for heavy and make it equipable on Gal medium - it would make Gal medium the ultimate AV king! Why should not Gal medium be king of everything - huh, CCP?

Here's a scenario. Let's say there are two players: Player A and Player B. Both players have the same weapon, and we will assume that weapon does 100 DPS for the sake of round numbers. The only difference between the two is that Player A equipped a complex damage mod. and player B equipped a complex shield extender. We will assume they started with a base health of 100 each also for the sake of round numbers. Player A and Player B both open fire on each other at the same time: who dies first?

Player A is doing 110 DPS vs a 173 eHP (66 shield extender + 10% skill bonus) enemy.
Player B is doing 100 DPS vs a 100 eHP enemy.

Player A would kill Player B in 1.572... seconds.
Player B would kill Player A in 1 second.

So basically, damage mods aren't as good as you seem to think they are. There would be an even larger disparity between the two if you consider that each damage mod suffers from stacking penalties, while HP modules do not, and then an even LARGER disparity if I used a complex armor plate as an example instead. Let's say that Player B equipped a complex armor plate instead.

Player A is doing 110 DPS to a 248 eHP (135 plate + 10% skill bonus) enemy
Player B is doing 100 DPS to a 100 eHP enemy

Player A would kill Player B in 2.54... seconds.
Player B would kill Player A in one second.

Look at that! The player with the plate kills the player with the damage mod more than twice as quickly!

CPU/PG upgrades, meaning we have a weak armor tank, meanig we have to dual tank.

Yeah, no thanks.

Now you see how I feel I don't want to have to stack plates to have enough ehp as you. You chose your suit because you want to armor tank I chose mine because I want to shield tank. Your double or triple damage mod fit is preventing me from getting the max hp out of my shields due to the fact I have to stack damage mods also so I can go toe to toe with you.