Here is the math to proof that **at the moment** the darkin form is stronger than the shadow assassin (armor and magic resist are not taken into account).
Going through every ability starting with **Q**
With **300 AD** Darkins Q is stronger as soon as the enemy has at least only ~835hp.
**shadow:** base dmg + 65% bonus dmg
135 + 300*0.65 = ~258 dmg
**darkin:** 50% total ad + 5% max health + 4% max health per 100 bonus ad
150 + X*0.05 + X*0,04*2 [2 is for ~200 bonus ad] = 258
X = 834,61 HP
Warrior: +60 attack damage
Youmuus: +60 attack damage
Tiamat: +20 attack damage
Lets say everyone's level 9. Lets take some runes +15 AD.
Kayn should be at around 240 AD (around 155 Bonus AD).
shadow Q dmg (with both hits) = ~470 dmg
darkin Q dmg (also both hits against an adc lvl 9 lets say caitlyn 1064 hp) = ~478 dmg
**Darkin is already stronger**
Both deal the same amount of damage but the shadow assassin can move while casting his W and it has 200 increased range (but the W doesnt follow him like Taric E does so its still not much easier to hit an enemy who runs away) while darkin has an AoE knock up.
No Bonus here for darkin (he already gets the %health dmg on Q). Shadow gets 30% more movement speed (from 40% to 70%) and cant be slowed inside terrain. This bonus is still so small compared to the base form E that it doesnt make the base E feel bad.
**With R its getting very interesting**
With **300 AD** (~190 bonus AD] shadow assassin deals 559 dmg.
Darkin's ult with 300 AD deals ~36% max health dmg.
This means the **enemy only needs 1552 hp for darkin to deal more ult dmg** than shadow assassin + darkin gets a heal of 70% of the enemy's max health + passive heal.
**using the early/mid example from the Q spell again**
(reminder: everyone's level 9, Kayn has 240 AD ~(155 Bonus AD), our enemy is cait (1064 HP))
shadow ult dmg = ~321 dmg
darkin ult dmg = ~321 dmg
At this point the exact same amount of dmg is dealt at 1063,018242 HP. If an enemy has more HP, the darkin ult is stronger.
I tested it on PBE. Against a target with ~100 armor (that was actually fighting as well not just standing still) I was able to release ~300 bonus magic damage with over 350 AD in those 3 seconds which is nothing since you have to stay out of combat for 8 seconds (or use your ult) to use it again.
Darkin on the other hand heals for 43% of the damage dealt with abilities to enemy champions (late game Kayn with 40% cdr has a 3 second cooldown on Q)
**tl;dr** In teamfights a titanic hydra, black cleaver darkin can all in into the enemy team, save himself with his insane ult heal and disappear through a wall while being much tankier and dealing the same amount of dmg to squishies and more dmg to tanks than the shadow assassin. Even in mid game darkin already deals the same amount of dmg to squishy targets with same items as the shadow assassin.