Kol vs. Radiance:
Let's analyze a level 5 of each ship (if nothing else, so that each has level 3 of at least one ability)...
Radiance:
Hull = 2200 + 90 x 4 = 2560
Shield = 1750 + 180 x 4 = 2470
Armor = 4.5 + .4 x 4 = 6.1
Shield mitigation = 65 +1.111 x 4 = 69.444%
Kol:
Hull = 3000 + 120 x 4 = 3480
Shield = 1250 + 135 x 4 = 1790
Armor = 5 + .45 x 4 = 6.8
Shield mitigation = 65 + 1.111 x 4 = 69.444%
Looking at just these stats alone (no abilities, cruiser protection, or tech upgrades), Kol clearly is better at surviving...it has better armor, more hull, and more HP overall...however, if we are testing resilience, we need to grant each capital ship its resilience ability...
Radiance:
Level 3 energy absorption grants +6 armor...that brings the armor up to 12.1, which is equivalent to a 1 / (1 + .05 x 12.1) = 62.3% damage multiplier....however, this only applies to hull, which represents about 51% of the total HP, so we could equate this to about an 80.8% damage multiplier overall...
Kol:
First off, let's consider the armor of the kol which is equivalent to a 1 / (1 + .05 x 6.8) = 74.6% damage multiplier...applied to only the hull (which is about 66% of the HP), that is equivalent to about an 83.2% damage multiplier overall due to armor...I'd like to point out that despite having less armor than the Radiance, the Kol still benefits almost just as much from armor because it has far more hull....
Level 3 adaptive forcefield grants 35% damage reduction...though this is dependent on antimatter use, let's assume the kol is using this ability continuously (so damage reduction applies all the time)...this is equivalent to a 1 / (1 + .35) = 74.1% damage multiplier...compounding this with the armor bonus, that gives the Kol a .741 x .832 = 61.6% damage multiplier overall...
By considering just level 3 of each ship's resilience ability, the Kol again clearly comes out as the winner with an 80.8% (Radiance) vs. 61.6% (Kol) damage multiplier...even if the Kol can't use its ability at all, the Radiance then only marginally beats the Kol (80.8% vs. 83.2%) with its damage multiplier...
However, the Kol has more HP overall (5270 vs 5030) so actually when one compounds the total HP and the average damage multiplier, they'll find the Kol to actually be superior...to show this, one would analyze the "time to live", which in general is HP / (DPS x damage multiplier)...for any given DPS, you'll find the "time to live" will be higher for the Kol given the noted HP and damage multiplier of each capital ship...
To sum this up, the Kol is superior to the Radiance (with energy absorption) in terms of resilience even if one doesn't consider adaptive forcefield...while the Radiance has more armor (with energy absorption), the Kol has significantly more hull and has more HP overall...if one considers adaptive forcefield, then the Kol is clearly far superior to the Radiance in terms of survivability...
Now, let us, however, consider tech upgrades...
Advent:
Shields +30%
Hull +30%
Armor +4.0
Shield mitigation +4% (shield bonus)
TEC:
Shields +20%
Hull +30%
Armor +6.0
These technologies result in the following changes:
Radiance:
Hull = 3328
Shield = 3211
Armor = 16.1 (includes energy absorption level 3)
Shield mitigation = 73.444%
Kol:
Hull = 4524
Shield = 2148
Armor = 12.8
Shield mitigation = 69.444%
Damage reduction = 35%
Let us determine the damage multiplier first for each ship (for this, I will assume for simplicity that max shield mitigation will always apply)...our general equation will be:
Damage multiplier = [(% of HP that is hull) x (1 / (1 + .05 x armor)) + (% of HP that is shields)] x (1 - shield mitigation %) x (1 / (1 + damage reduction %))
Radiance = 20.5%
Kol = 22.5% / 1.35 (damage reduction) = 16.6 %
Again, even with technology upgrades, the Kol seriously outperforms the Radiance...
Let us consider the affect of early game support cruisers (hoshiko and iconus guardian)...
The Iconus Guardian absorbs 33% of all incoming damage, putting the Radiance at a 13.5% damage multiplier...the Hoshiko adds 15 hull/s, which we need to equate to DPS...using the inverse of the Kol's damage multiplier, we would find that a Hhoshiko essentially "cancels out" 90.4 DPS....to give some perspective, this is equivalent to about 11 LRMs (considering the damage table of Antimedium vs. capital armor)...
If one considers these support cruisers, at low levels of damage the hull/s is more useful while at high levels of damage the damage reduction from the Iconus Guardian is more useful...let us set up our equation by comparing the "time to live" for each ship...remember, time to live is Total HP / (DPS x damage multiplier)....let us use D to represent DPS...
Radiance ttl = Kol ttl
6539 / (D x 13.5%) = 6672 / ((D-90.4) x 16.6%)
If you do the algebra, you find that D = 531.1 DPS...this means that if the capital ship is taking more than this number, the Radiance + Iconus Guardian is better...if the ship is taking less than this number, the Kol + hoshiko is better...
Since 531.1 DPS is like 64 LRMs, I'd say in general the Kol is in better shape...in a situation where you'd face more firepower than that, you'd have to consider many other thinks like TK push, embolden, and probably a higher level capital ship (which means finest hour and +15 hull/s for the Kol)...
One final consideration is culture bonus...however, if we consider culture bonus, then I think we should assume a defensive situation, in which case I would consider repair platforms to be fair game....
Advent gets an additional +6% shield mitigation, but TEC has a much better repair platform (40 hull/s vs. 30 hull/s)...I'm not going to run the numbers, but the +6% shield mitigation probably would be better than the extra 10 hull/s granted by a repair platform...of course, a TEC advocate could argue that with cielo's embolden and a SB's docking booms, the Kol would be better...Advent could counter argue with a domina's +25 hull/s and a Progenitor's shield regeneration, and TEC could come back with Finest Hour's +15 hull/s 1/3 of the time and a Dunov's shield restore...and we could go on and on and on, not really getting anywhere...
In general though, I think it is quite clear that stand alone, Kol is unquestionably more resilient...even without the use of adaptive forcefield, the Kol is very competitive with a Radiance using energy absorption...I think late game with a full battleball, a Radiance would be harder to kill but any Advent ship should be harder to kill than its TEC counterpart if protected by a battleball...
The last important consideration is the phase missile block granted by the Kol...in a TEC vs. Advent matchup, the Radiance is only going to be more resilient if protected by an entire late game Advent fleet...however, vs. Vasari the Kol would unquestionably outperform the Radiance due to Advent's inherent weakness against phase missiles...
This is not to say the Kol is better overall than the Radiance or is more useful...however, I think it is quite clear the Kol is the most resilient of the two (and probably the most resilient single object in the game other than a starbase)...