I would not be able to distinguish between the mass of 2 objects with 1 and 1.001 kg by just having them in my hands, but this does not mean their masses are incomparable.
Here is a discussion about this between me and Anthony DiGiovanni. @Jim Buhler, you may be interested in it.
Here is a discussion about this between me and Anthony DiGiovanni. @Jim Buhler, you may be interested in it.