IIRC when you include duty cycle AAF comes out to a ~35% increase in total firepower, which is flux free and concentrated at the start of an engagement in most cases. Burn drive has some value for fast hunter cruisers, but the effective flux/firepower advantage is significant.
Right. The fact that it can be used to start the engagement means that a roughly equivalent ship begins on its back foot and never really recovers. The effect this has on the AI is substantial, so much so that it can mean the difference between squeaking out a win (Pirate Eradicator) and not taking any damage at all (standard).
If AAF is considered ~30% boost in DPS, then the standard Eradicator should be about 30% more expensive to field than the Pirate version. Unsurprisingly, this is 22 relative to 17. That's a bit of an oversimplification, of course, but Burn Drive doesn't have the same battlefield impact as AAF by a large margin, in my opinion, at least not on a ship with 70 base speed. You could make an argument that AAF on a Dominator wouldn't necessarily be "better" (I still think it might be) but the Dominator's slow base speed necessitates Burn Drive a lot more than the Eradicator does.