Skill Discussions

The armors to V and the shields to IV is the general rule these days.

Reasoning is:
Many armor tanked fits use a passive EANM, so the skill affects quite a lot of ships you will fly.

NOT very many shield fits use passive modules. Most will use the active version called Adaptive Invulnerability Field II
Invulns used to get a benefit from the comp skills.... not any more though

If you find yourself using a passive shield fit on a regular basis, train up the corresponding shield comp to V. I do believe the bonus is worth the time, for specific fits. (PvE Tengu/exploration comes to mind.)

Summary:
* Armor Resist Compensation Skills: level 4 adequate, but all level 5 worthwhile (EANM).
* Shield Resist Compensation Skills: level 4 adequate if used, but level 5 EM most worthwhile.

Details:
* Armor tanks commonly use passive EANM that cover all resists, so it is desirable to maximize these skills.
* Since shield tanks have 0% base EM shield resist, fitting an EM resist amplifier is common when an EM field hardener won't fit because of fitting resource (i.e. CPU, grid) limitations.
* EM shield resistance amplifier are sometimes fitted on cloaky ships, so they don't have a resist hole while cloaked.
* There are niche uses for shield resist amplifiers, where maximizing all the skills is worthwhile.

Note that things haven't changed in 2 years.

Patch notes for EVE Online: Retribution 1.1, Deployed on Tuesday, 19th of February 2013. wrote:

Modules

* Armor and shield compensation skills no longer give any bonus to active armor or shield hardeners.

Resists are powerful especially in the context of a fleet with logi in it. The logi is essentially taking the place of buffer, so slowing down incoming damage is more useful. Most PvP fits will consider the use of logi in a fleet, and concentrate far more on resist profile than raw HP in a buffer. You need enough buffer to survive an alpha volley, but again, reducing incoming damage proves more beneficial than just eating full DPS and trying to patch the hole left in your shields/armor.

So IV is pretty much the de facto requirement for compensation skills. The fact is that in any combat, but especially PvP, you WILL take damage. The question then becomes about how you choose to mitigate that damage. Reducing incoming DPS means less reliance on buffer.
For purely PvE purposes, this is simple, as a given NPC faction deals a specific main DPS with a smaller amount secondary. So obviously if you are in Serpentis space, for example, skilling up for Kinetic and Thermal are important while EM and Explosive are not.
However, PvP requires an omni-tank since you never know what will be shooting you in the face, and since it's here you are likely to see logi support- you will be relying less on buffer and more on remote reps- you want to focus on resists both for fitting and for skills.

as noted before its fit specific
armor has the greatest use thx to eanm and nano plating so lvl 4 is pretty much a must and lvl 5 is a nice to have skills.
For shield i used shield mission ships which were cap injected and that's why i needed passive resistance and then its a nice skill to have but on average they aren't that high on the list

Pretty much this.

i think the main exception to that rule is em (shield comp) as frigates profit the most from them.

Passive shield amps are used plenty in PvE where you're facing heavy neuts. Still Armor to 5 ; Shield to 4 with EM to 5 when possible as mentioned earlier.

In something like c1-c2 wh's it is.

Since the tengu? No not so much.

I have both Armor and Shield Compensation skills at V. But that's because I'm just maxing out at this point.