This should be up to date

http://elderscrollsonline.wiki.fextralife.com/Mundus+Stones

The way I look at it is this, increases to your Critical Strike Damage is not as important as increasing your base damage. Why? You have to Crit to get the extra damage, but your crits are based on your Base Damage. So, you get more damage all the time by choosing Warrior whether you crit or not and get close to the same boost in Crits when those do happen. If you have a character that is sitting at 70% or 80% Critical Chance already, then it might make sense to boost Crit Damage.

Now, it might be useful to get the Mundus that increases your Critical Strike Chance, that might be worth something depending your build.

Yeah it was thought that the shadow stone was broken. At 1.6% increase to crit dmg it's not even an option.

"Warrior's, come out and Plaaaaayaaaaay"

why or?

why not just exploit and have both. YAY FOR ZOS!

I was just thinking about this a couple of hours ago. I mainly play a Sorcerer so was thinking about Apprentice compared to Shadow and Thief but the same concept applies.

The base damage formula is
Base damage = a*(Stam+b*W)(1-Mit)*Attacker_CP * Defender_CP
where a and b are coefficients with b~10.5, W is your weapon damage and Mit is the mitigation. We can roll the Attacker_CP and Defender_CP into the coefficient a without any worries for the analysis. The mitigation is also not important but I'll keep it here for the moment to show you that it can evetually be neglected

The base damage when using the Warrior stone is
Base damage_Warrior = a*(Stam+b(W0+W1))(1-Mit)
Here I have separated your weapon damage component into weapon damage from Warrior stone and associated buffs, W1, and weapon damage from everything else, W0

The average damage with the Warrior stone is
Damage_Warrior = (1-C)*Base damage_Warrior + C*M*Base damage_Warrior
where C and M are your critical chance and critical damage modifier, respectively. With some arithmetic, we obtained
Damage_Warrior = a*(Stam+b*W0)(1-Mit)(1-C+C*M) + a*b*W1*(1-Mit)*(1-C+C*M)

The base damage when using the Shadow stone is simply
Base Damage_Shadow = A*(Stam+b*W0)*(1-Mit)
From this, we can obtain the average damage
Damage_Shadow = (1-C)*Base damage_Shadow + C*(M+S)*Base damage_Shadow
where I have used S for the Shadow stone. Again some maths leads to
Damage_Shadow = a*(Stam+b*W0)(1-Mit)(1-C+C*M) + a*(Stam+b*W0)(1-Mit)*C*S

In order to figure out when the Warrior mundus is preferred over the Shadow mundus, I shall just subtract Damage_Shadow from Damage_Warrior

Damage_Warrior - Damage_Shadow = a*(1-Mit)* [ b*W1*(1-C+C*M) - (Stam+b*W0)*C*S]
a and (1-Mit) are always positive so you simply need to evaluate the second term. I don't have a stamina build so I'll put in some typical values for a Sorc to show you an example

The Apprentice like the Warrior stone confers 167 Spell damage. W1 includes all Spell damage buffs as well so as a Sorcerer I typically run a 26% buff due to Expert Mage and Surge. Thus W1 = 167*1.26=210. We'll stick with a b value of 10.5. My crit chance, C, is 0.42 and my critical damage modifier, M, is 1.51 (I have 1 point in Elfborn). My Magicka is about 40k and my Spell damage from other stuff is around 2k. So my calculation would be

10.5*210*(1-0.42+0.42*1.51) - (40000+10.5*2000)*0.42*0.12 = -397

in my example I should use the Shadow stone. You don't have to take into account divines since it can be factored out.

On a semi-related note have you considered using the Thief mundus stone?

Rather briefly the maths is as follows
Damage_Shadow = (1-C)*Base Damage + C*(M+S)*Base Damage
Damage_Thief = (1-C-T)*Base Damage + (C+T)*M*Base Damage

Damage_Thief - Damage_Shadow = Base Damage ( T*(M-1) - C*S )

Thief is better than Shadow when, T*(M-1) - C*S > 0
This is equivalent to fulfilling the equation below
(M-1) / C > 60/59

Back to my example,
(1.51-1) / 0.42 > 60/59 is true thus the Thief is better for me.

Note that there may be some problems with your critical damage modifier because it seems ZOS rounds it to 2 decimal places so sometimes it doesn't appear to change...

Hope this answers your question!

Summary:
If [ b*W1*(1-C+C*M) - (Stam+b*W0)*C*S] > 0, use Warrior
where b = 10.5, W1 is Weapon damage from Warrior stone including and buffs, C is crit chance, M is crit modifier, Stam is your Stamina, W0 is weapon damage from everything else and S is the Shadow mundus stone (0.12)
otherwise use Shadow

If (M-1) / C > 60/59 is true
where M is crit modifier and C is crit chance then use Thief otherwise use Shadow.

Ok... too many numbers floating around... so what is the new critical % that Thief offers? I believe on PTS it was 12% but they'd discussed reducing it before it went Live.

So at wich point The shadow is a better option than the warrior?

@srlamasnrb18_ESO

If [ b*W1*(1-C+C*M) - (Stam+b*W0)*C*S] < 0, use Shadow
where b = 10.5, W1 is Weapon damage from Warrior stone including any buffs, C is crit chance, M is crit modifier, Stam is your Stamina, W0 is weapon damage from everything else and S is the Shadow mundus stone (0.12)

If that didn't make sense do the following steps
1. Buff yourself with food and skills
2. Record your weapon damage. This is W0.
3. Get the Warrior Mundus
4. Record your weapon damage, call this W2. Subtract W0 from W2 to otain W1.
5. While buffed record your Critical Chance and Critical Damage Modifier. The simplest way to get your Critical Damage Modifier is to buff yourself appropraite and hit any mob till you get a crit and a non crit. Divide the crit damage by the non-crit to get your Critical Damage Modifier.
6. Put it all the numbers in the top equation
7. If it is negative use Shadow otherwise use Warrior.

Here are some made up numbers if that process didn't make sense.
Weapon damage while buffed , W0 = 1000
Weapon damage while buffed and with Warrior Mundus, W2 = 1200
Then W1 = W2-W1=200
Crit chance is 55% and Critical Damage Modifier is 1.55. Stamina is 30000
Calculate
10.5*200*(1-0.55+0.55*1.55) - (30000+10.5*1000)*0.55*0.12 = 62.25
It is positive so use Warrior