In addition to fragrances, they differ only in the presence of the so-called "pink" tax in the price of women's shampoos. If you have noticed, "women's" products are always several, and sometimes quite significantly more expensive. True, I still feel most acutely the spread in price not in relation to shampoos, but in relation to shaving machines and shaving gel, so I prefer to take men's ones. The properties are identical, but the "brutal" design does not bother me at all. Moreover, with real savings over 500 rubles.
There is no real difference in the composition - the main components are the same (you can make sure by reading the composition in the store of two products from the same line m and w), the difference is only in the fragrance, the color of the liquid and the box. Menthol is added to some men's shampoos, this is rarely found in women's shampoos. But, there are shampoos for dandruff, deep cleaning, for colored hair, with silicones or super-natural. There will be more differences, but they are still subtle. Products from one line will be 99% the same.