Difference between viral and human genetic material
To sum up: If we are not talking about chromosome organization, nucleotide sequences and overall genome architecture (which are incomparably different in eukaryotes and [even their] viruses) the differences in the genetic material are as follows:


viruses are much more diverse in their choice of genetic material, which is in the cornerstone of viral higher systematics. It can be DNA or RNA, single- or double-stranded, circular or linear. Animals, in turn, possess only double stranded DNA as their genetic material: linear dsDNA for the nuclear genome and [usually] circular dsDNA for the their mitochondrial genomes.
DNA termini pose a special problem for the maintenance of the molecule and show very unusual organization in terms of DNA sequence and structure. Repetitive terminal sequences of eukaryotic chromosomes have 3'-overhangs, which form a special quadruplex form of DNA. Termini of viruses are naturally much more diverse and are (nearly?) never of the same structure as in Eukaryotes. [Circularization/decicrularization is one of the mechanisms recruited by viruses]. (Deng et al 2012)
DNA methylation is normally present in varying degrees in animals and in vertebrates most of the cytosines in CpG dinucleotides are methylated. Viruses differ considerably from one another in this respect, but it seems that smaller viral genomes are generally under-methylated and larger genomes do not show under-methylation, although it depends on the stage. This conclusion is based partly on indirect evidence that CpG motifs are considerably much less frequent in smaller viruses. Integrated "genetic parasites" like retroviruses are normally rich in CpG and are highly methylated. (Hoelzer et al 2008)
although I couldn't find relevant literature, I'd hypothesize that the highly packed genetic material in viral particles may potentially exist in more compact forms of the DNA helix (in dsDNA viruses). Most of the dsDNA in cells is present in a so-called B-form, but there are more compact A-form and less compact left-turned Z-form (there are other forms, most of which are biologically not relevant). (cf. Wikipedia for an introduction)