Instantaneous vs Duration
The primary benefit of animate objects is that it lasts for more than one round. The result of this is the conservation of spell slots. Instead of having to cast fireball multiple turns in a row, you can get the high DPR of animate objects over multiple turns.
Certainly, damage on the first turn is more impactful than sustained damage since it removes enemies that could potentially attack your party on those later turns, but the drastic reduction in later turn damage when resorting to cantrips after a big fireball makes animate objects better even despite this fact.
To demonstrate, let's evaluate the damage output as you requested in "when it is better to use animate object to deal damage, based on how numerous, heavily armored and dextrous the opponents are" and then contrast the first turn damage with the damage over the course of 4 turns (even accounting for the diminished impact of later damage).
Turn 1 Damage
To start with, if you can hit 3 or more targets with the fireball, it will deal more damage on turn 1 than animate objects almost no matter what (unless AC is especially low and Dexterity is especially high). Along the same vein, fireball against one target is typically worse than animate objects, but not to quite the same degree. Here is the chart of the damage output of fireball (green indicates better damage when the animated objects have advantage, yellow when they don't, and orange when they have disadvantage):
As a rule-of-thumb metric, you can use AC 20 as a break point for when to use fireball against one target (AC 15 when the animated objects will have disadvantage, and AC 25 when they will have advantage). The Dexterity has less of an impact than AC when it comes to damage comparison of these two spells.
If you are hitting 2 targets, it becomes more complicated.
For this situation, disadvantage makes fireball almost always better, but deciding whether to use fireball or animate objects is more complex. For a rule-of-thumb, use animate objects without advantage when their Dexterity save + 8 is less than their AC, and use animate objects with advantage when their Dexterity save + 14 is less than their AC. This doesn't quite work on the extremes, but is a valid approximation.
Later Turns Damage
To account for the persistent duration of animate objects, let's compare the damage over 4 turns, while reducing the impact of the later turn damage by 25% for turn 2, 50% for turn 3, and so on.
For the sake of this comparison, I am assuming the fireball casting is followed up by a 2d8 cantrip that also targets Dexterity (for simplicity).
Here is the new comparison for a 1 target fireball:
When considering the persistent damage of animate objects when compared to cantrips on later turns, fireball is only better against 1 target when the animated objects will have disadvantage and AC is at least 20.
Here is the new comparison for a 2 target fireball:
Here, the new rule-of-thumb is that you should use animate objects even with disadvantage when Dexterity save + 10 is less than their AC, without disadvantage when Dexterity save + 17 is less than their AC, and with advantage almost always.
3 target fireballs and 4 target fireballs are similar skewed towards animate objects. It isn't until 5 target fireballs that we get a more borderline case similar to the 1 round 2 target fireball:
If you really need a rule-of-thumb for this specific case, you can use Dexterity save + 12 for advantage, and Dexterity save + 6 without advantage. However, at this point it is clear that the persistent damage of animate objects more than compensates for the lesser 1st turn damage when compared to fireball unless you can hit 6+ creatures with the fireball.