Do women receive the same reward as someone who performs ablution at home and then goes to the mosque, given that they pray in their homes?

The aforementioned Hadith (definition) in Sahih (definition) Muslim states that whoever purifies himself in his home and then walks to the mosque to perform an obligatory prayer, one of his steps erases a sin and the other raises his rank. This reward includes both men and women. However, for women, it is better and brings greater reward to pray in their homes, based on the Prophet's (peace be upon him) saying: "Do not prevent your women from coming to the mosques, though their houses are better for them," and his saying: "A woman's prayer in her house is better than her prayer in her courtyard, and her prayer in her private chamber is better than her prayer in her house."