Do alms in Islam favor the rich over the poor as the rich have more to give away?

Zakat is one of the earliest forms of state taxation. This was a notable change from previous forms of taxation which rulers levied on their subjects at their discretion, raising and lowering taxes as they pleased. In these instances, more often than not, heavy taxes were levied on the poor and light taxes, if any at all, were levied on the rich. In contrast, Islamic law imposes a set tax, zakat, on the rich and middle classes and exempts the poor.

Another difference is that alms in Islam are not simply financial transactions, but also an act of worship just like prayer and fasting. In fact, in all the books of the four Sunni schools of jurisprudence, zakat falls under the section of 'ibadat [devotional acts] and not mu'amalat or [social dealings]. Zakat is therefore an act that draws Muslims close to God the Almighty and by so doing, purifies their wealth which is the exact linguistic and technical meaning of the word zakat.

During the Prophet’s lifetime, the poor complained to him that they felt that the rich earn more rewards because the zakat they pay gives them extra opportunity to draw closer to God the Almighty. Upon hearing this, the Prophet (peace and blessings be upon him) instructed them to increase their dhikr [remembrance of God] and say ‘Subhan Allah’ [Praise be to God], ‘Alhamdullah’ [all praise be to God] and ‘Allahu Akbar’ [God is greatest] thirty three times after each prescribed prayer. This would thus give them an equal status with the wealthy who were able to pay zakat. This demonstrates that zakat is a devotional act and the ultimate goal of any devotional act is to draw closer to God the Almighty. The one who is best in this is the one who is higher in rank as the Quran says: "And the best of you with Allah is the one that is most Allah fearing" [49:13].

Fear and mindfulness of God is not only based on one devotional acts but can be fostered through other ways. This is why the intention is of great importance in Islam. It is the basis of all actions as the well-known Prophetic hadith says: "Verily, all actions are judged according to their intentions, and each man will have what he intended.”

Accordingly, a poor person who wishes to give out money but is unable, is rewarded for his intention and receives the same reward as the wealthy. At the same time, it is possible that a wealthy person intends ostentation by giving money and is rewarded accordingly.
And God the Almighty knows best.