Here is the main problems with Shields vs. Armor.

1.) Cost CPU/PG per eHP
Okay, here is the conversion rate. Most suits run between 4-5x CPU per PG. Taking that into effect, lets make a universal cost number. CPU is the base unit, and PG is 4.5 Unit per PG point.

So here are the universal costs of shields and armor modules, with an eHP ratio attached to it (eHP / Universal cost = eHP per unit)

Basic extender: 24 eHP / 31.5 U = 0.76 HP per unit.
Basic Plate: 93 eHP / 19 = 4.9 HP per unit.

Adv Extender: 36 eHP / 63 U = 0.57 HP per Unit
Adv Plate: 121 eHP / 47 U = 2.57 HP per Unit

Complex Extender: 73 eHP / 103.5 U = 0.71 HP per Unit
Complex Plate: 148 eHP / 84 U = 1.76 HP per Unit

See the problem? This is the appeal of armor tanking. You get the most HP for your CPU/PG with armor tanking.

2.) Speed Penalties

Basic Plate: 2%
Adv Plate: 3%
Complex Plate: 5%

Let the record state this: A complex Plate's sprint speed penalty can be offset by a SINGLE BASIC KINCAT.
Try this, take a Min scout and put on a complex plate. Look at it's sprint speed, and then put on a basic Kincat. It jumps back up to 8.3, which is 0.01 m/s slower than where it was in the first place.

It is so easy to fix the speed penalties on armor suits, and made easier due to the fact that armor suits typically have higher PG than shield suits, which makes almost no sense, as you will see in part 3.

3.) PG and CPU costs compared to eachother.
Seems redundant, but it's not.

Shield Modules are supposed to be high CPU, low PG right?
Armor Modules are supposed to be low CPU, High PG right?

WRONG AND WRONG.

Look at the earlier stats. Basic Extenders cost 3x more PG than a basic plate, and 8 more CPU. Adv Plates and Adv Extenders are equal in PG while Complex only has a 1 PG difference.

The CK.0 and GK.0 Assault have the same base CPU/PG stats, but the Gallente will always have an easier time PG wise, due to their eHP modules costing far less on their fit (see part 1.). Shield modules are harder to fit, give you less eHP, and their supporting modules are so CPU heavy, you almost have to use a low slot to give yourself the CPU you need (90 CPU for a complex Energizer, but a Complex armor rep costs less CPU than an extender and the same PG.)

4.) Shield Regen isn't enough to save the shields.
I could go on about this for ages. Shield regen is the only saving grace for a shield tank, as it literally beats armor rep silly in time to regen. However, armor tanks almost always run around with either logi's or rep hives, negating this downfall, and shield regen simply isn't fast enough for a frontline suit.

Which is why everyone armor tanks Armor suits and Dual Tanks Shield suits. Simply because eHP armor modules are more effective in your lows than Regulators or Kincats (The two "biggest strengths" of shield tanks are regen time and mobility. Speed won't let you avoid fire, and the Regulators don't give enough of a bonus.)