Average damage is statistically equivalent given your sample sizes... In fact, the only outlier on that entire chart is the 8% difference in peak Doomspike II damage. You could easily interpret the results in a variety of ways given the lack of known equations or a baseline test... For instance, if you assume that a percentage increase in attack will equate to a roughly equivalent or slightly greater increase in damage output (consistent with FFXI mechanics), you would expect a 6.6-7% increase in damage with the second set over your nonexistent baseline. If we also assume that your STR is compared to the enemy's VIT such that an increase of ~4 STR will increase a melee attack's base damage by 1 (again consistent with FFXI mechanics), 37 STR would give 9~10 base damage. If your "fSTR" was low in the second test, this could give... up to a 6.6% increase in damage over baseline assuming neutral fSTR in the second test. Hmm. Funny how that works.
I would suggest observing damage peaks on low level monsters with varying STR levels (as low as possible, then increasing it incrementally) if you're interested in testing my suspicions since fSTR would likely be easier to establish initially than the inner workings of the attack/defense equations, plus it may give you a value for capped attack/def function to work with. Would happily do it myself but unfortunately my current system can't run FFXIV.
EDIT: Disclaimer: I am not asserting that the equations
must be the same, only that they are likely the same given that it was many of the same people within the same company. I realize that I only provided an example that supports my theory, but it was only put forward with the intent of demonstrating plausibility.
Another way to observe potential correlations would be comparing the difference between these sets on a job with a lower base damage weapon, bearing in mind the possibility that STR could conceivably cap lower in this situation.