Both male and female privilege is real. Which one you feel is better depends on how you view life. Men are free to act, take charge, have many sexual partners and have it seen as a good thing. We are groomed into well paying professions and are expected to be progressive in business. High expectations to success, not allowed to show feelings and sanctioning against passiveness are downsides that can be stressing.
Women have less expectations, and are more free to express identity, personal ideas, and feelings. They still don't have to make careers to succeed and can 'save' themselves by breeding and becoming mothers. It is still acceptable for women to stay at home and do nothing, and to take years of to spend with their kids. Getting a partner that takes care of them, unrelated to their income level, is seen as a success. Women have the favor in divorce and in parenting rights. A woman can also make complete success on her looks, and climb social ladders easier than men (if they are pretty). Downsides are the early sexualization and objectification of their looks, usually starting at puberty around 11-12. Ugly women are punished for being ugly, since being pretty is seen as a defining trait in women. It is difficult for them to succeed in business and break through upper levels of management, and they are usually demeaned by men in any setting, unless said men want sexual favors from them. Being physically weaker they are at risk of being overtaken and threatened by men. We put the responsibility of assault on the victim so the freedom of movement and use of intoxicants is more limited for women, and punishment is justified by men if women put themselves in the same position as them in social spheres such as nightclubs and pubs.