Which is better, performing ‘Umrah or giving charity to the poor and needy when it is difficult to do both actions?
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If you mean the obligatory charity (i.e. Zakah), then it is better than ‘Umrah without doubt. However, if it is voluntary charity, then, in principle: Hajj and ‘Umrah are better as they involve spending money along with other acts of worship like Tawaaf (circumambulation of the Ka'bah), Sa‘y (walking between Mounts As-Safaa and Al-Marwah), Thikr (remembering and mentioning Allah), prayer, and Talbiyah (the Hajj-related chant).
Nonetheless, if there are people who are in need of a person's charity or if he has needy relatives and he cannot combine giving charity and performing Hajj and ‘Umrah, then charity is better in such a case.
On the other hand, An-Nasafi, the Hanafi scholar said, "Hanafi scholars have said that voluntary Hajj is better than charity."
Al-Hattaab the Maaliki scholar said, "Maalik was asked whether he preferred Hajj or charity and he replied, 'I prefer Hajj, unless it is a year of famine.'"
Shaykh Al-Islam ibn Taymiyyah said, "If a person has needy relatives, giving to them in charity is better and so is the case if there are people who are in need of the charity. If both Hajj and charity are voluntary, then Hajj is better because it is an act of worship that combines both physical and material aspects. Likewise, offering Udh-hiyah (a sacrificial animal given on 'Eed)) and ‘Aqeeqah (a sacrificial animal given for the new-born) is better than giving their value in charity."
Ash-Shawkaani said in his commentary on the Hadeeth of the very best deed which was collected by Al-Bukhari and Muslim , where the Prophet (may Allah exalt his mention), mentioned belief then Jihaad then Hajj: "This Hadeeth is proof for those who view that voluntary Hajj is better than charity."
One who ponders over the conditions of the Ummah nowadays realizes that there are many people in need of charity. There are many Muslims all over the world who cannot find food, drink or residence. Thus, giving charity to such people would take precedence over (voluntary) Hajj and ‘Umrah.
Allah Knows best.