Men have more chiyuvim in mitzvos, but that doesn’t mean we’re on a higher madreigah than women.
Kohanim, though, are on a higher madreigah than Leviim and Yisraelim. The brachah for birchas kohanim is ??? ????? ??????? ?? ????, which connotes a higher level of kedushah.
Women, on the other hand, according to some Rishonim, can say the brachah of ??? ????? ???????? even on mitzvos for which they’re not obligated, become the p’tur isn’t based on a lower level. Even the Rishonim who disallow the brachah, as I recall, object to the lashon of ??????, because they’re not commanded.