How does the organization of genetic material differ in prokaryotic and eukaryotic organisms?

Prokaryotes have one circular strand of DNA whereas eukaryotes have several strands of linear DNA.
Prokaryotes are single celled organisms without membrane enclosed organelles (specialized compartments/structures in the cell). Therefore the DNA resides in the cytoplasm. Prokaryotes have double stranded DNA molecules clustered into a so called nucleoid. Next to this chromosomal DNA prokaryotes often also have small circular pieces of DNA with only a small amount of genes these are called plasmids and can replicate independent of the chromosomal DNA.
Eukaryotes have a specialized membrane enclosed organelle that contains the DNA this is called the nucleus. Each nucleus contains multiple linear molecules of double stranded DNA organized into 23 pairs of chromosomes.
The DNA of prokaryotes is much more compact because it contains much less non-coding DNA in and between the genes compared to eukaryotes. In prokaryotes genes can be transcribed together into one mRNA these groups of genes are called operons.
In eukaryotes most of the DNA does not code for a protein. It was once termed ‘junk DNA’ but we know now that it has some important regulatory functions. In eukaryotes there are no operons each gene is transcribed separately into its own mRNA.
In both eu- and prokaryotes the DNA molecules are condensed with the aid of different . In eukaryotes the DNA is wrapped around proteins called histones. In prokaryotes the HU-protein fulfills this task.