Increased attack speed vs. "Extra" damage?

I am perhaps misunderstanding: I thought "more" damage is better than "increased" - but does this also apply to IAS?
Context: spirit offering (extra chaos damage) vs flesh offering (IAS), both in roughly the same amount. Flesh is considered the "offensive" offering, and it surely seems it: FO is more than 3x as strong as Haste. But what about the extra damage gained as chaos from SO? If all of my minions are doing mostly physical (zombies + evangelists + SRS (half physical))? Is FO still "better" for damage?

Flesh offering isn't better because of attack speed, it's movement speed.

Speed is a separate multiplier from increased damage when it comes to calculating DPS. Thus, it has its own diminishing proportional return curve separate from that of increased damage, but which works the same way mathematically.

Existing 0% increased damage -> further x% increased damage = x% more dps
Existing 50% increased damage -> x% increased = (x/1.5)% more
Existing 100% increased damage -> x% Inc = (x/2)% more

Existing 0% increased attack speed -> further x% increased attack speed = x% more DPS
Existing 50% increased attack speed -> x% increased = (x/1.5)% more
Existing 100% increased attack speed -> x% inc = (x/2)% more

The tricky part is that because PoE and most ARPGs are about making choices between different multiplicative options, you have to judge multiplier power in terms of a change relative to what's available. There's kind of a self-fulfilling prophecy here; since sources of increased damage tend to be higher, and attack speed lower, a lower amount of attack speed will have the same multiplicative effect as a higher source of increased damage. At level 1, of course, x% increased is always the same as x% more. However, I believe most endgame DPS-focused builds end up with about 500% increased damage and 100% increased speed. In that case, multiplicative attrition for increased damage is 1/6, while attrition for attack or cast speed is 1/2; the ratio between them is 1/2:1/6 or 1:3, which means attack speed becomes 3 times its increased in more DPS compared to increased damage; 20% increased attack speed becomes equivalent to 60% increased damage in terms of more DPS (both give 10% more DPS in this example).