That's actually a bit tricky to answer. The 'default' answer is of course to go with the PDT. However one should also know why, and under what limits such an answer would be correct.
The PDT itself is easy enough. 4% less damage, or rather 40/1024 less damage, which can be applied to any physical attack, including those where Vit/Def would have no effect whatsoever (eg: 1000 Needles).
For the other side we need to factor in the full stat differences, including defense.
Koenig Cuirass: 65 def, 20 vit. Effectively 75 def with 20 Vit for purely stat purposes.
Versa Hauberk +1: 63 def
So the difference to be accounted for is 12 defense and the effect of 20 vit.
The value of 12 defense depends on the mob's attack and your existing defense, such as if you're using Defender (seems likely if you're gearing for defense like this).
Starting defense is likely to be around 300 (typical DD stuff), 400 (def gear + Defender) or 500 (def gear + Defender + defense food), given that you're using War and thus don't have the Defense Bonus traits of Pld. Will assume 400, but look at things at 300 and 500 as well.
You then need to know how that correlates with the mob's attack. Aside from buffs the mob may have, I would generally expect mobs to have an attack around 450-500 (for anything of high enough level for this setup to be a consideration).
That puts the mob's Ratio at a range varying across: 1.5-1.667, 1.125-1.250, or 0.900-1.000.
Add 12 defense and the Ratio varies as: 1.442-1.603, 1.092-1.214, or 0.879-0.977.
That gives a damage reduction value equivalent to: 3.87%-3.84%, 2.93%-2.88%, or 2.33%-2.30%.
So at low starting defense, that 12 def is worth almost as much as the -4% PDT on its own. At higher amounts of starting defense, though, it's worth notably less.
However we then must make another realization: The 400-500 defense values assume use of Defender. Defender is a multiplier on defense. We added 12 to our base defense, so the value with Defender included is actually +15 def, not +12. Things get a bit fuzzy at that point based on which actual defense value you use, but in essence you should be getting at least 3.5% damage reduction.
Of course you could also get up to ~400 def using a defense atma before adding Defender, which puts the value of additional def back down around the 3% mark. On the other hand +def gains significant extra value when defending against crits (note above that the higher the mob's Ratio, the more valuable +def is).
Then we need to factor in the Vit.
Assuming mob fStr works the same as players', you can have a negative fStr equal to the WRank of the weapon, which is its base rating divided by 9. Most NMs of note seem to have an effective weapon rating somewhere around 200 to 300 damage. In theory you could get their fStr down to the -22 to -33 level.
At 0 dStr you have an fStr of 2. Every 4 Vit you add should reduce that by 1 point. Given the limit based on the weapon rating, that means adding Vit would be effective up to around +96 to +140 Vit over the mob's Str.
How much str does the mob have? No idea. Based on known mob stat calculations, we can estimate that most will have a str similar to a standard naked character with a few extra levels under their belt, but it's hard to be sure (and is explicitly not the case with certain NMs such as Kirin).
If that is actually the case, we can assume that most mobs won't have a str over ~100. We can thus limit the useful value of player Vit (for conservative estimates) to about 200, though though it could potentially go as high as 250-300.
Given high-end zone bonuses you should be getting cruor buffs of +70. As a war your innate Vit is going to be fairly low. Overall I would not expect a non-gear total of more than 150, which leaves room for ~50 vit in gear before reaching overloaded status. Barring any other sigificant amounts of Vit in gear, +20 from the body should be comfortably usable.
We then look at how much 20 Vit actually reduces damage. 20 Vit would be -5 fStr. For a 200-300 base damage weapon, that's a reduction of somewhere around 1.5% to 2.5%.
Overall, the vit+def of the Koenig should equate to a general damage reduction of around 4.5% to 5.5%, just a smidge better than the Versa. With a high starting player def and a high weapon damage rating for the mob, overall reduction can fall below 4%.
The other stat issue to consider is that the Versa also has +14 att, compared with the Koenig's -10 str. If you explicitly want to reduce the damage you're doing while also reducing damage taken, it would seem the Koenig is the best choice on both fronts. It also has the slight survivability bonus of an extra 60 HP, which is nice.
On the other hand, if you still want to get a bit of offense out of your gear set then going with Versa is the better option, while only slightly behind defensively.