The math is a bit complex to get the right answer but here goes.
First you need to get your damage per hit which would be:
total damage per hit = (base weapon damage × skill damage) × (1 + primary stat / 100) × (1 + first damage bonus) × (1 + second other damage bonus etc) × (1 + monster vulnerability bonuses)
to simplify lets just go with (100 base damage x 100% skill damage) x (1 + 1000str/100) and ignore the rest of it.
So DPH would be 100x11 = 1100 without the added str and 100x12.6 = 1260 with.
Then we need to work out attacks per second which is:
attacks per second = weapon tooltip attacks per second × (1 + dual wield bonus + other gear and skill attack speed bonuses)
so for a sword with a speed of 1.40 we would have 1.4 x (1+0) = 1.4 using no IAS and 1.4 x (1+0.15) = 1.61 with the 15% IAS.
Now we put them together.
1100x1.61 = 1771 dps with IAS
1260X1.4 = 1764 with the extra STR
..well based on this seems like you are right in that the IAS should work out better for you. It may be a scaling issue, which I doubt, since STR and IAS dont have dimnishing returns, or it could be one of the bugged IAS items and you arent actually getting the bonus... or I fucked up somewhere.. which is also likely.
Ah, yes that would do it. The crit chance makes a big difference for you especially since you have the extra crit damage as well.
ETA: after running the numbers again with your specific stats (and what I am assuming is ~691 damage weapon) the strength still comes out on top even without the added crit chance. So it would seem that my original math was off due to scaling issues after all.
For TL;DR guys - IAS is better on Two-Handed Maces/Axes/Mighty Weapons ; STR on everything else, because the extra-armor is nice. If you're using Frenzy, disregard IAS. Always cut a balance, you can't have'em all.
You like country lore, don't you?
Not only is your post inherently wrong since whenever you stack either stat, the other one becomes tremendously better, but any 1h +life on hit build easily benefits a whole lot more from +IAS than any 2h build does.
As for Bombay: Not only is the Strength on your neck better considering your low overall Strength but it also adds a good amount of crit. Since you can easily push crit damage very high, you can easily squish out way more than 1% DPS per 1% crit while AS is pretty much hard capped at a maximum of 1% DPS per 1% AS.
Basically this. With 800 STR that +164 accounts for ~18% increased damage. Yet with 1200 STR it drops to ~12% increased damage. Where as the 15% IAS is always ~15%.
Also thanks for simplifying my math, i did indeed get a bit over complicated.