One of the most interesting things to emerge from a rigorous comparison of the biology of aging between species is the role of cell membrane composition, as outlined in the membrane pacemaker hypothesis.
The membrane pacemaker hypothesis predicts that long-living species will have more peroxidation-resistant membrane lipids than shorter living species.
Resistance to oxidative damage is of particular importance in mitochondria, cellular power plants that progressive damage themselves with the reactive oxygen species they produce as a byproduct of their operation - and that gives rise to a chain of further biochemical damage that spreads throughout the body, growing ever more harmful as you age. Less damage to the mitochondria should mean slower aging, and thus more resistant mitochondrial membranes should also mean slower aging.
The evidence for this view is good, and continues to accumulate. See, for example, investigations of the biology of naked mole rats and other long-lived species with unusual biochemistries. As this recent review paper notes:
The relationship between membrane fatty acid composition and longevity is discussed for (1) mammals of different body size, (2) birds of different body size, (3) mammals and birds that are exceptionally long-living for their size, (4) strains of mice that vary in longevity, (5) calorie-restriction extension of longevity in rodents, (6) differences in longevity between queen and worker honeybees, and (7) variation in longevity among humans. Most of these comparisons support an important role for membrane fatty acid composition in the determination of longevity. It is apparent that membrane composition is regulated for each species. ... The exceptional longevity of Homo sapiens combined with the limited knowledge of the fatty acid composition of human tissues support the potential importance of mitochondrial membranes in determination of longevity.
This, I think, is one of the best illustrations for the merits of comparative studies of the biology of aging. Absent data from a range of different species, it seems unlikely that the membrane pacemaker hypothesis would have gathered as much interest in the community. Here's a related commentary:
Comparative biology plays several roles in our understanding of the virtually ubiquitous phenomenon of aging in animals. First, it provides a critical evaluation of broad hypotheses concerning the evolutionary forces underlying the modulation of aging rate. Second, it suggests mechanistic hypotheses about processes of aging. Third, it illuminates particularly informative species because of their exceptionally slow or rapid aging rates to be interrogated about potentially novel mechanisms of aging. Although comparative biology has played a significant role in research on aging for more than a century, the new comparative biology of aging is poised to dwarf those earlier contributions
For my part, focused as I am on the biotechnologies of human longevity, I see the most important aspect of this discussion being that it draws more attention to mitochondria, mitochondrial structure, and the prospects for mitochondrial repair. Clearly it is the case that human mitochondria serve well for the first few decades of life, and it is only later that the level of mitochondrial damage becomes large enough for degenerative aging to become materially apparent.