I have been trying to research the differences between human and pig DNA. I've had no luck finding any kind of information on this matter.

Well, you have to decide for yourself what aspects of the genomes you want to concentrate on. You can start with comparing the sizes of haploid or diploid genomes, the number of genes, the number of chromosomes, the percentage As and Ts in the genome. A human and a pig share quite a lot of genes and whole gene families, which only differ slightly in their DNA sequences between the species. This is something one would expect, because in some cases one would a have hard time telling one from the other. What the genomes also share is of course that they are, as well as all other genomes, just long stretches of repeated four nucleotides A, T, C and G. A good place to start:

Pig: Ensembl genome browser 60: Sus scrofa - Whole genome - Karyotype
Human: Ensembl genome browser 60: Homo sapiens - Whole genome - Karyotype