The growing interest in fermented dairy products is due to their health-promoting properties. The use of milk kefir grains as a starter culture made it possible to obtain a product with a better nutritional and biological profile depending on the type of milk. Cow, buffalo, camel, donkey, goat, and sheep milk kefirs were prepared, and the changes in sugar, protein, and phenol content, fatty acid composition, including conjugated linoleic acids (CLAs), as well as antioxidant activity, determined by ABTS and FRAP assays, were evaluated and compared. The protein content of cow, buffalo, donkey, and sheep milk increased after 24 h of fermentation. The fatty acid profile showed a better concentration of saturated and unsaturated lipids in all fermented milks, except buffalo milk. The highest content of beneficial fatty acids, such as oleic, linoleic, and C18:2 conjugated linoleic acid, was found in the cow and sheep samples. All samples showed a better antioxidant capacity, goat milk having the highest value, with no correlation to the total phenolic content, which was highest in the buffalo sample (260.40 ± 5.50 μg GAE/mL). These findings suggested that microorganisms living symbiotically in kefir grains utilize nutrients from different types of milk with varying efficiency.