Rav Hirsch doesn't say that women have more enthusiasm for religion in general than men, he says they have more enthusiasm for THEIR job - “more faithful enthusiasm for their God-serving calling.” (Vayikra 23, Levy trans.) But they have a different calling. You can't really compare the two. It would seem that his statement is building off of the Midrash that women have zrisus for mitzvos. This is likely referencing emotion and not necessarily action. The Magen Avraham (Zies Ra'anan on Yalkut Shimoni, Shmuel 1:1) says that women are exempt from positive time bound commandments because their yetzer TOV is not as strong as that of men and if commanded the women wouldn't do those commandments. Source here: https://belovedcompanions.blogspot.com/2013/05/magen-avraham.html So they have enthusiasm for their job but wouldn't necessarily have that for the men's job. We might note (my own thought) that most of the men's special mitzvos are masculine (building a succah, wearing the same black leather box on one's head every day, going outside into the heat and cold for minyan, sticking to a precise schedule (Shema) no matter how one feels.
