Suppose you are investigating the genetic basis of a rare disease that causes degeneration of neurons?
Phrozen
You have brain tissue from normal individuals and from a few unrelated patients who died from the disease. Should you look at differences between DNA or proteins to search for the cause of the disease?

I would say that both could be possibilities, because you’re never sure where the mutation is till you see it. mRNA could just as easily be the source, but so could be the foldings of the proteins or the placement of the various nucleotides in DNA.
Anyone would know you have to look at both.
Then create a hypothosis and experiment with each one.
The first question to ask is what causes the degenertion of the neurons. If it is iron build-up, excess copper, loss of myelin, ect. This can help narrow gene and protein candidates.
You then want to make sure it has a genetic cause. So you would need to determine the mode of genetic transmission in a population and/or familes before you embarked on a genetic study. With any luck you can determine what you are looking for: a rare dominant, rare recessive, polygenetic, or multifactorial.
After that, a good place to start looking for a gene is with a linkage study, but you will need to see if you have enough samples for the statistical power required for these analyses. It enables scanning of the whole genome to look for regions common to the cases but not usually found in controls.
There are also techniques for scanning a large fraction of all the proteins (2D gels, ICAT, ect.). This can give you other targets that may be different in cases. In the end the question is what is the cause of the disease. The protein data may give markers for the disease, but it may not allow for you to determine the cause. Once you have the basis for the degeneration, the candidates should be narrowed down considerable.
Good Luck!
In practical terms you would probably start with looking at differences in DNA. This is because comparing DNA of the sick and healthy individuals is much faster and requires less material. If you find a mutation in the sick compared to the healthy that would be the best place to start.
If you didn’t find any likely mutations, you could start to look at the proteins. Since you don’t know which proteins to look for (or maybe the symptoms give you a start) it may take you awhile to find what you’re looking for. If the disease is caused by a prion, you would have a very hard time to identify it, but there wouldn’t be any use in looking at the DNA.