I do not believe women are on an intrinsically higher spiritual level than men. Based on experience the people who say it have a very hard time coming up with any place in Chazal, Rishonim etc. that say it. I was told that one of the gedoily hador in the 1970s was so upset when he first heard a speaker say that women “don’t need to do” Mitzvas Esey Shzman Grama because they are on a higher level that he publicly got up and protested (in middle of the speech) the zilzul in Mitzvas (Esey Shzman Grama)
If there was any real source that gadol would have known about it.