|MadSci Network: Genetics|
The number, size, and structural organization of every organism's chromosomes are very distinctive, particularly for cytogeneticists who are expert in their interpretation. Although they might not be able to precisely identify the organism of origin simply by examining a chromosomal "spread", they probably could tell whether an individual chromosomal spread could have come from a particular organism, as long as that organism's chromosome organization has been sufficiently characterized.
In your particular example, onions have 16 diploid chromosomes (8 pairs), whereas chickens have 78 diploid chromosomes (39 pairs), as reported in this handy table from Kean Univ. showing the Chromosome Numbers of Selected Organisms. For the chicken, 9 of the haploid chromosomes are classified as macrochromosomes and 30 as microchromosomes, with the ZW (sex) chromosomes included in the macrochromosomes, according to The Chicken Gene Map from the Nat'l. Academy of Sciences. I'm not sure why the chicken chromosome no. is listed as '77,78' in this table. I have seen elsewhere reported that the onion has only 14 diploid chromosomes, too, but Kean Univ. seemed like a more reliable resource.
So given this background information, the short answer to your question is; 'yes, there is "a visual difference between plant (onion) and animal (chicken) DNA"', in that the chicken's are greater in number and complexity than the onion's. BUT, these differences require an experienced cytogeneticist with a highly trained eye and specialized equipment to distinguish them. The chromosomes also have distinctive sizes, structures, and "banding patterns" when stained, which enable the cytogeneticist to characterize them.
In addition, if you scan the Chromosome Numbers of Selected Organisms Table, you'll notice that plants usually have fewer chromosomes than animals, but not always (e.g. salamanders vs. peanuts). Therefore, visual differences between plant and animal DNA cannot be generalized.
This may be more information than you needed, but hopefully I've touched upon an explanation for your science fair project somewhere in here. Thank you for the interesting question,
Jeff Buzby, Ph.D.
Children's Hosp. of Orange Cnty.
MadSci Genetics Network
Try the links in the MadSci Library for more information on Genetics.