The other answers have covered a lot of other things, but a few additional options to consider.
Area Control
10 small objects under your control occupy 10 spaces of the battlefield. Creatures you don't want to move through those squares now can't do so without dealing with that obstruction.
What's more, if the enemies try to avoid dealing with your animated objects by running past them, well every single one has a reaction to use for an attack of opportunity.
Damage Soak
Ogre McOgreson and his friends deal a ton of damage when they hit the party's Rogue and a single casting of fireball is not going to stop them. With a single casting of Animate Objects, you can create at least 250 hit points* worth of minions to soak mitigate a ton of damage.
*I say 'at least', because if an animated object has 3 hit points left and the ogre hits for 15 damage, all that excess damage is overkill that your party doesn't have to deal with.
Selective Damage
A scenario where your allies are all mixed up with a bunch of enemies is sure to just leave everyone irritated if you launch a fireball into the fray. The ability to have Animate Object pick and choose who gets stabbed is much less likely to create a friendly fire issue.