What is the difference between an animals DNA and a plants DNA ?

There are lots of differences between animal & plant DNA, but what they are depends on at what you are looking.

Chemically, plant, human, animal, bacteria, fungi, and even many viruses
have identical DNA. DNA is composed of a backbone made from deoxyribose
(A sugar) and phosphate. The individual base pairs that encode the
genetic information are adenine, guanine, cytosine, and thymine (AGCT). A
base pairs with T, and G base pairs with C, which defines specificity for
DNA, and allows one strand to direct the replication of an exact
complementary strand, so an organism can make another set of DNA and
divide/reproduce. This was elegently demonstrated by Meselson & Stahl, a
observation for which they recieved a Nobel Prize, and it agreed perfectly
with the Watson & Crick model of DNA.

So, in many ways, structurally, chemically, and in the nature of
reproduction/synthesis, plant DNA and animal DNA are very similar, if not
identical. So much so, that when we place genes from plants and animals
inside of bacteria, they will often follow those instructions and produce
a foreign protein instead. This is how human insulin for the treatment of
diabetes is produced in a bacteria.

The main difference between plant and animal DNA is in the
organization of genes and the size of the total genome, or how many base
pairs of DNA the organism has. As a rule, plants tend to have much larger
genomes than their animal counterparts, and they have a larger portion of
garbage and intron DNA. Very few genes are present in this DNA, and it
tends to contain regions that are spliced out, or perhaps serve a
structural role in the shape, packing, and placement of the genome.
In terms of size for example, the human genome contains about 3-4
billion base pairs of DNA, whereas corn or maize, is perhaps a less
complex organism contains a similar number of base pairs. Some pine trees
and lilly plants contain 10-100 times as much DNA as a human, most of
which does not appear to encode any genes.

The manner in which DNA is chemically modified in the cell is
different in plants and animals. Although many of the same modifications
occur in both plants and animals, such as adding methyl (CH3) groups to
the DNA, occurs under different circumstances or for different reasons.

-by Matt Champion from http://www.madsci.org/-