Gram-positive foodborne pathogens such as Listeria monocytogenes and Staphylococcus aureus can grow in a wide variety of foods, including raw milk. The aim of the study was to compare the growth of L. monocytogenes and S. aureus inoculated in donkey and cow samples of raw milk during a storage time of 11 days at 8 °C. Moreover, the study aimed to evaluate the influence of lactic acid bacteria (LAB) content on the growth of the two microbiological populations considered. LAB content was lower in raw donkey milk than in raw cow's milk during the entire analyses; on the other hand, pH levels were higher in the donkey milk rather than in the cow's milk, although both values showed a decrease at the day 11. S. aureus showed no significant differences in the two types of milk. From day 0 to 11, L. monocytogenes increased from 3.68 ± 0.02 log CFU/mL to 6.31 ± 0.07 log CFU/mL and from 3.64 ± 0.04 log CFU/mL to 4.59 ± 1.04 log CFU/mL, in donkey milk and in cow's milk, respectively. Our results showed that donkey milk is a more favourable matrix to support the growth of L. monocytogenes than cow's milk.