The rule of thumb is a Def Buff is equivalent to 2 times a Resist buff.
Reasoning - Assume 50% chance to be hit by critter doing 100 points of damage.
No buffs - 50% x 100 = 50 points of damage per attack.
10% Def buff - (50 - 10)% x 100 = 40 points of damage per attack.
20% Resist buff - 50% x 100 x (1 - 0.20) = 40 points of damage per attack.
Also numerous critters have attacks that debuf defense which leads to as someone put it, "cascading defense failure". The more they hit you, the easier it becomes to hit you again. Not bad against a normal single critter since they attack slower than the debuff usually last but in groups or by an AV/EB, it can hurt a lot, soft cap or not. Fewer critters have damage resistance debuffs.
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The rule of thumb is a Def Buff is equivalent to 2 times a Resist buff.
Reasoning - Assume 50% chance to be hit by critter doing 100 points of damage.
No buffs - 50% x 100 = 50 points of damage per attack.
10% Def buff - (50 - 10)% x 100 = 40 points of damage per attack.
20% Resist buff - 50% x 100 x (1 - 0.20) = 40 points of damage per attack.
Also numerous critters have attacks that debuf defense which leads to as someone put it, "cascading defense failure". The more they hit you, the easier it becomes to hit you again. Not bad against a single critter since they attack slower than the debuff usually last but in groups it can hurt a lot. Fewer critters have damage resistance debuffs.
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Ok, so I did understand that all correctly, including the issue of cascading failure (which I understood as "the more you get hit, the more you get hit"). Is that the only reason Sturdies have roughly half the effectiveness of Lucks?
I am just thinking would 20/30/40% or 25/35/45% be that bad for Sturdies to be? Would that be gamebreaking or something? Or even in the range of Rages, since they would be offsetting (much like how Insights and Lucks oppose each other)? Even at those numbers they would still pale next to Lucks, just not so terribly.
11 months of all-nighters, messy feeding sessions, bath fighting and realizing just how good my son's lungs work, and I am still convinced he is the crowning accomplishment in my life. What in the blue HFIL is wrong with me?
QR
Basically, what FX above me said.
If you are already softcapped to defense, then lucks will really only benefit you when fighting against large groups that have a -def component to their attacks or are +2 or higher to you.
I'd still carry a few for protection against the cascading failure, but if you are softcapped, sturdies will serve you better in the long run.
For starters it's worth noting that Damage Resistance itself resists Damage Resistance Debuffs, so you're more likely to keep what protections you have.
But any amount of hand-waving theory isn't as good as just seeing something in action. If you take a character (starting with less than soft-capped Def 
) and put it in a stressed combat situation, a single purple or a single orange will give you about the same increase in survivability.
I'd recommend going to somewhere like the northeastern forests of Bloody Bay with their large Banished Pantheon zombie spawns. You can find spawns of the same, large size and level close together. Try fighting them, then try it with one or the other small insp. They give about the same benefit in those repeatable situations.
"Normally", you are correct: lucks are better than sturdies.
There are circumstances where Sturdies are useful, though. If you've already got a lot of (either defense or resistance) getting more of the same thing helps, until you hit the cap. So if you're running a Fire Tank with, I dunno the numbers so I'm making them up for simplicity, 75% resistance to something and no defense:
one Luck gives you 12.5% Defense, and you get hit 3/4 as much.
one Sturdy takes you from 75% to 85% Resistance, and you take 3/5 as much damage (15% of total, instead of 25%.)
Two Lucks produce misses half the time; two Sturdies get you to the 90% Res cap (tanks cap at 90%; almost everyone else caps at 75%) and you take 40% as much damage.
If you have an autohit attack, like the Envoy of Shadows delivers (I think he still autohits; he definitely used to) no amount of Luck helps.
If you are at the defense softcap, usually no amount of Luck helps.
At those points, if it looks bad, eating a handful of big orange pills will give you significant benefits.
(Most of the time, I end up taking small insps two or three at a time...)
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"Normally", you are correct: lucks are better than sturdies.
There are circumstances where Sturdies are useful, though. If you've already got a lot of (either defense or resistance) getting more of the same thing helps, until you hit the cap. So if you're running a Fire Tank with, I dunno the numbers so I'm making them up for simplicity, 75% resistance to something and no defense:
one Luck gives you 12.5% Defense, and you get hit 3/4 as much.
one Sturdy takes you from 75% to 85% Resistance, and you take 3/5 as much damage (15% of total, instead of 25%.)
Two Lucks produce misses half the time; two Sturdies get you to the 90% Res cap (tanks cap at 90%; almost everyone else caps at 75%) and you take 40% as much damage.
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Agreed, but that is comparing a character with no prior defense to stack on top of to a character with prior resistance to stack on. Additionally, you are using the scenario of tanks, who benefit by being able to even get to the 90% Resistance cap, something only Brutes can do, as well. Everyone is capable of using the 45% Defense number.
Also, there is the issue of Resistance only being that good to the one type the Armor tends to specialize in (Fire damage in the case you mentioned, maybe S/L if the character took Tough). Defense tends to be a bit more inclusive. I look at my above example as a demonstration of this.
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If you have an autohit attack, like the Envoy of Shadows delivers (I think he still autohits; he definitely used to) no amount of Luck helps.
If you are at the defense softcap, usually no amount of Luck helps.
At those points, if it looks bad, eating a handful of big orange pills will give you significant benefits.
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So, then, regardless of AT or starting value (save zero), stacking is usually better than layering until you hit whatever the cap is? Makes sense.
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(Most of the time, I end up taking small insps two or three at a time...)
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Or I plow down a big one. Either way, from the same starting point (I tend to need them more on my Regen character who has little Resistance or Defense after MoG), Lucks are going a lot further for me. Just seemed odd that in a vacuum, 2 Small Lucks are better than 2 Large Sturdies (25% Defense versus 40% Resistance).
All this was discounting or calling it paid for that Defense also means you miss the secondary effects of attacks while sometimes being susceptible to the RNG hating your guts. Those Sapper beams, Carnival Masks, and Vanguard debuffs are evil (although sometimes a Defense player looks at a group of Family or Council with machine guns and thinks, "Dirty son of a...").
11 months of all-nighters, messy feeding sessions, bath fighting and realizing just how good my son's lungs work, and I am still convinced he is the crowning accomplishment in my life. What in the blue HFIL is wrong with me?
and, by extention, the whole "Defense versus Resistance" idea in general.
I have looked for other threads about this, but either there were none or my search-fu is pitifully weak.
Personal anecdote... I just finished getting IOs on a Shield Scrapper and got him to the softcap (or as close as I choose to get him to that point), so I started swapping out the Lucks I had in my inspiration tray for Sturdies like usual (because I figure the lucks cannot do too much more for me, save help me against groups of Debuffers), and start checking out the numbers.
For Sturdies, it's 10/15/20% Resistance.
For Lucks, 12.5/25/33% Defense.
Now, I am always trying to learn (you know? Forever a student of the game and whatnot), so please correct me if I am wrong, but does this strike anyone else as out of whack?
If I recall correctly, isn't a percent of Defense greater than a percent of Resistance? Also, doesn't being at the softcap (45% Defense to a type or vector) mitigate nearly 90% of incoming damage and completely bypass the negative effects of any attack with that type or vector (For example, if someone has 45% Smashing Defense, they have it against not only attacks like Negative/Smashing/Melee, but also Fire/Smashing/Ranged or Electric/Smashing/AoE). Even at the AT's cap for Resistance, only the damage of the matching type could be reduced (so a character with 90% Smashing Resistance would eat the full Negative, Fire and Electric damage in my above examples, and that is if said character is a Tank or Brute).
If all my following logic is correct so far, then why is the Luck family not only absolutely better in not only magnitude but also the amount of damage mitigation it provides?
Maybe I am looking at this from the wrong angle. I know that even with all that Defense, if an attack gets through, it will hurt. I also know that there are far more things that debuff Defense than Resistance (although the ones that debuff Resistance are heavy debuffs). However, if someone can get 12% Defense on their own (not difficult with the power options for Defense and the disparity between Resistance and Defense IO Bonuses, but that is for another day), that Phenomenal Luck is about to let them get away with something things they should not have any business messing with. For Defense-based Armor sets, even a small Luck could put them in that territory.
For those that like Resistance, even a Robust will usually not drive someone to their Resistance cap unless they previously slotted for it, and then would only give them capped Resistance against whatever type they already had.
So I guess what I am trying to ask is why is there such a disparity between the two inspiration families?
11 months of all-nighters, messy feeding sessions, bath fighting and realizing just how good my son's lungs work, and I am still convinced he is the crowning accomplishment in my life. What in the blue HFIL is wrong with me?