Given the option, is there a greater mitzva of Hachnassat Orchim or inviting guest to one’s home for men guest or women guest?

Bikurei Shai (Avos 1: 5) explains the saying of Yose ben Yochanan: “Let your house be wide open, and let the poor be members of thy household.” Followed by “Engage not in too much conversation with women” meaning that it may indeed be preferred to welcome lone women more than men, when place is limited. Otherwise, one should follow the ways of Avrohom Ovinu ans Sarah Imenu, that invited both and each took care of their own. In general we find that the Torah mentions to care for an Almanah or widow and does not mention an Alman at all, who can usually take care of himself. Horav Yaakov Hirschman’s Shlit’a is that the above has other factors that should be considered such as the age of the sons at home, etc.