Since that leggings nowadays can be found in every single shop there is and there is almost no brand or generic brand name manufacturer that does not make them, the decision should be made based on fabric alone. In terms of fabric, there are many possible choices, most popular and probably also most available fabric would be a blend of spandex, polyester, cotton and nylon, whereby the mix can wildly vary, but the end product does not seem to be that different. In this case, the best thing that you can do is try them on and see how you feel wearing them. It is very likely that you will wind up having at least a pair of these.
Additional versions exist in plain wool, which are preferred by people who have problems wearing synthetic fabrics and even silk. Silk leggings tend to be expensive, sometimes it is cheaper to purchase silk in bulk and have someone tailor you a pair. There are the knitted leggings, which were popular in the eighties and are still preferred by some dancers and exercise aficionados. Finally, there are the latex leggings, which I mentioned earlier, but latex in general requires not only getting used to, but requires proper handling. Not everybody is interested in spending time preparing latex leggings for being worn, but such preparation and the actual wearing of latex in general make the ordeal worth your while. Leather leggings do exist, although it is almost always faux leather being used, the difference to leather pants is next to non-existent, due to the rigidity of the material. Unless you are really looking for exactly that, you should not consider leather and similar for leggings at all.