Humans, mice and rats are almost genetically similar. All the three species are approximately 85-90% similar.
As you mentioned, mice are preferred for the simple reason that they are small and breed easily with short pregnancies. They can be housed easily, are relatively easy to handle and transport. Moreover, researchers can manipulate the mouse genome, model specific diseases, test new drugs, and investigate the genetics of diseases before trying them on human. Also, mice are extremely diverse, meaning that commercial breeders can select for individual traits to create inbred strains with unique characteristics. For example, the CBA mouse has a low incidence of mammary tumour development, whereas the BALB/c nude mouse is immunodeficient, since it lacks a thymus. These kinds of breed-specific properties are useful, as they allow researchers to focus on specific diseases.
Modifying mouse DNA is a powerful method for creating animal models of human disease. Techniques like the Cre/lox system and the CRISPR gene editing tool allow researchers to delete, activate or repair genes, thus recreating human disease in the mouse or examining what happens when they correct a mutation. You must have heard about “knock-out” mouse where in the gene is either removed or inactivated, and the "transgenic" mice where the mice are made to express human genes or carry human cells. In this way, researchers can create “humanized” mice that respond physiologically almost like us, letting researchers look at the way disease changes a human body and how it responds to treatment.
So, mice are a cost-effective and an efficient research tool providing so many options because of which they are preferred by researchers for in vivo experiments.
On the other hand, rats are quite different in social cognition, which can be important in research for disorders such as schizophrenia, autism spectrum disorder and mood disorders. Rats are superior at maze-learning, show stable performance in longer cognitive tests. They behave differently in terms of habit formation, impulsivity and other situations related to mood, addiction, and some psychiatric disorders. They show more compulsive and addictive behavior than mice. So, you may use rats to study behavior in psychological experiments. They have a larger brain than mice and they are more intelligent and less timid than mice.
You may have observed that researchers have increasingly used mice models more often than rats only because of their superiority as genetic models. The first recombinant mouse model was identified much earlier than the rat model. But now gene editing technology are available for both mice as well as rats, and so researchers will have more options to find an appropriate rodent model for their research.
I agree genetic relationship is a key issue, but I think there is more important taxonomic detail available today than just the raw genetic similarity. So the Last Common Ancestor of humans and rats (or mice - or rabbits for that matter) was probably a stem member of euarchontoglires, about 90 million years ago. In other words, mice, rabbits and rats are roughly equally related to humans (so choosing between them might be based more on other characteristics such as sociality, cost etc.).
By contrast, say for dogs, the LCA with humans belongs to the boreoeutheria, with an LCA time perhaps 10-20My earlier, so dogs are somewhat less well matched; and in the other direction, the LCA for old world monkeys and humans would be the stem group of the catarrhini, about 35 Mya, and for chimps maybe around 6Mya (making chimps and monkeys by far the most related, but leading to correspondingly greater ethical issues).
By the way, it's worth noting that there are two sources of indefiniteness in the dates. One is lack of knowledge, heavily affecting the older dates (maybe 10My or so), subject to improvement as more fossils are discovered and better dating is applied. But for the more recent dates, the greater difficulty is that taxonomies on the fine scale are actually networks rather than trees, so that even the definition of LCA is a bit fuzzy. For chimps, for example, a reasonable value could be anywhere between about 4Mya (last exchange of genetic information) and 7Mya (when the trees fully merge). This source of indefiniteness is unlikely to disappear.
The consensus is that mice and humans share approximately 85% of their protein-coding genes, while rats and humans share roughly 90% of their genes
The differences in genetic similarity often arise due to the focus on protein-coding genes versus non-coding regions of the genome. The genome of mice was sequenced in 2002 by the Mouse Genome Sequencing Consortium, revealing a high degree of genetic conservation between humans and mice, especially in genes related to basic biological functions. Similarly, the rat genome was sequenced shortly thereafter, with findings indicating a slightly higher genomic similarity to humans in some respects, such as disease pathways (Gibbs, R. A., et al. (2004). Genome sequence of the Brown Norway rat yields insights into mammalian evolution. Nature, 428(6982), 493-521).
1. Handling and Breeding: Mice are smaller, easier to house in large numbers, and breed prolifically, making them ideal for genetic studies, particularly in controlled environments.
2. Genetic Manipulation: The availability of well-established tools for genetic manipulation, such as transgenic and knockout models, has made mice a more convenient model organism than rats. Techniques like CRISPR/Cas9 have been successfully applied to both species, but mice still dominate in terms of genetic studies (Singh, P., et al. (2022). Advances in the genetic manipulation of rodents using CRISPR/Cas9 technology. Journal of Genetics and Genomics, 49(3), 275-284.).
3. Diverse Inbred Strains: Mice have a wider range of inbred strains available, allowing researchers to study a variety of genetic conditions, which adds to their utility in research involving genetic diversity.