Is it better for woman to go out to the Eid prayers or to stay at home?

It is better for women to go out to the Eid prayer. This was enjoined by the Prophet (peace and blessings of Allah be upon him). 

Al-Bukhaari (324) and Muslim (890) narrated that Umm ‘Atiyyah (may Allah be pleased with her) said: The Messenger of Allah (peace and blessings of Allah be upon him) commanded us to bring them (women) out on (Eid) al-Fitr and (Eid) al-Adha, and to bring out adolescent girls, menstruating women and virgins, but the menstruating women were to stay away from the prayer, but were to witness goodness and the gathering of the Muslims. I said: “O Messenger of Allah, what if one of us does not have a jilbaab?” He said: “Let her sister lend her a jilbab.”  

Al-Haafiz said: 

This shows that it is mustahabb for women to come out and attend the Eid prayers, whether they are young or not. 

Al-Shawkaani said: 

This and similar hadeeths indicate that it is prescribed in sharee’ah for women to come out to the prayer-place, with no differentiation between virgins and non-virgins, young or old, menstruating or otherwise, so long as they are not going through ‘iddah (following divorce or death of their husband) or their coming out will be a cause of fitnah or they have an excuse.  

Shaykh Ibn ‘Uthaymeen was asked: what is better for a woman, to come out to the Eid prayer or to stay at home? 

He replied: 

It is better for them to go out to Eid prayer, because the Prophet (peace and blessings of Allah be upon him) enjoined that the women go out to the Eid prayer, even the adolescent girls and virgins – i.e., women who do not ordinarily go out. He commanded them to go out, and he told the menstruating women to go out but to keep away from the prayer-place. So menstruating women should go out with other women for Eid, but they should not enter the place where the Eid prayer is offered, because the Eid prayer-place is a mosque and it is not permissible for a menstruating woman to stay there, but it is permissible for her to pass through or to take something she needs from it, without staying there. Based on this we say: women are commanded to go out to the Eid prayer and join the men in this prayer, because of the goodness, dhikr and du’aa’ they may experience there. 

Majmoo’ Fatawa al-Shaykh Ibn ‘Uthaymeen, 16/210. 

He also said: 

But they must go out looking decent, not wearing adornment, makeup or perfume, so that they may combine following the Sunnah with avoiding fitnah. 

What some women do of wearing adornment, makeup and perfume is because of their ignorance and negligence on the part of their guardians. This does not cancel out the general shar’i ruling, which is that women are commanded to go out to the Eid prayer.