With same gravity constance everything fall down at the same speed, but only in a vacuum. In an atmosphere there count the air resistance of an object, even if they are made of the same material and weight, an iron sphere of 1 kg fall faster than a iron sheet of 1 kg.

Except if you could measure exactly the speed of objects falling in a vacuum, the heavier object would appear to fall faster due to the gravitational pull on the Earth. You’re forgetting the Earth falls toward the object too.