If you look at what is actually happening, Featherfall reduces the speed of the object to where it's equivalent to falling a few feet.
Feather fall instantly changes the rate at which the targets fall to a mere 60 feet per round (equivalent to the end of a fall from a few feet)
Objects falling a few feet can still deal damage, though.
Objects that fall upon characters deal damage based on their size and the distance they have fallen. Table: Damage from Falling Objects determines the amount of damage dealt by an object based on its size. Note that this assumes that the object is made of dense, heavy material, such as stone. Objects made of lighter materials might deal as little as half the listed damage, subject to GM discretion. For example, a Huge boulder that hits a character deals 6d6 points of damage, whereas a Huge wooden wagon might deal only 3d6 damage. In addition, if an object falls less than 30 feet, it deals half the listed damage. If an object falls more than 150 feet, it deals double the listed damage. Note that a falling object takes the same amount of damage as it deals.
Since the object, due to the spell, only counts as falling a few feet, it would deal half the damage listed in the table.
However, since it also says the falling object takes the same amount of damage as it deals, and the spell prevents the object from taking damage, that might also imply that it deals no damage.
I think it ultimately comes down to the GM ruling, but either case you're looking at maybe half of 3d6 damage, max.
-- edit --
Just as characters take damage when they fall more than 10 feet, so too do they take damage when they are hit by falling objects.
I think SevenSidedDie mentions the above rule in his comment. Personally I don't think this means the minimum distance an object should fall is 10 feet. I would expect that if this were the case, it would be mentioned explicitly in the rule.
(Also, while living beings can attempt to catch themselves from short drops, a brick will make no such attempts and still hurts like hell if you drop it on your head from a foot away.)