I guess, we are talking about mammals here (because in other organisms leveling up of expression on sex chromosomes happens differently: e.g. in flies females express both X chromosomes, while fly males express their single X at twice as high level).
In embryo proper the decision of whether to inactivate maternal or paternal X seems to be at random. This inactivation adjusts level of expression of genes on X to be in the same ball park as on autosomes and in the same ballpark between males and females. Neither farther nor mother cares about which copy of X gets inactivated in individual cells of an embryo.
When we say that a gene is imprinted, that means only one copy of the gene is expressed but, to the contrary of what happens with X, maternal or paternal origin of the expressed copy is predetermined (so there is no randomness in which copy is inactive). Imprinting is usually a property of genes expressed during embryonic development and it is related to tug of war between farther and mother's interests: the farther "wants" embryo to take as much resources from the mother as possible (so paternal copies of some genes tend to be highly expressed), while mother wants not to give too much to one embryo, so that she can raise many more progeny (so maternal copies of some other genes tend to be highly expressed). This whole thing is interestingly described Matt Ridley book The Red Queen: Sex and the Evolution of Human Nature.
Note, that to confuse matters a little bit, in placenta of female embryos it is always the paternally inherted X that gets silenced, so the whole X chromosome is imprinted in extra-embryonic tissues of female embryos.
And in males X chromosomes do not get inactivated, since many genes are present solely on X chromosome and not on Y, so inactivating the only copy of X chromosome is lethal.