Is Allah's love greater than a mother's love for her child? Or is Allah's love less than that?
I have no idea whether you are using 'Allah' here as a generic Arabic term for God or asking for an explicitly Islamic conception of theism and divine love?
Because I don't know what your looking for specifically, I will attempt to answer within both an Islamic framework and my own Christian theistic concept.
In terms of Islamic theology, there is a Hadith which extols divine mercy as a force exceeding that of a created mother's care for her offspring:
Narated By 'Umar bin Al-Khattab : Some Sabi (i.e. war prisoners, children and woman only) were brought before the Prophet and behold, a woman amongst them was milking her breasts to feed and whenever she found a child amongst the captives, she took it over her chest and nursed it (she had lost her child but later she found him) the Prophet said to us, "Do you think that this lady can throw her son in the fire?"
We replied, "No, if she has the power not to throw it (in the fire)."
The Prophet then said, "Allah is more merciful to His slaves than this lady to her son."- Sahih Bukhari.
Not expressly a reference to divine love but appears to answer your question, I would think, as "love" is a divine attribute of Allah in Islam just like mercy.
The Christian conception is basically the same, the Jewish Tanakh poses the following rhetorical question from the perspective of God:
"Can a woman forget her nursing child, or lack compassion for the son of her womb? Though she may forget, I will not forget you!" (Isaiah 49:15)
However, I would caution that what it means for a supreme and purely spiritual Divine Being to "
love" is, arguably, qualitatively different than the human experience of love; inasmuch as human love is a consequence of powerful hormones acting as neurotransmitters in the brain, such as the "warm-fuzzy" bonding chemical oxytocin, which is released through acts of physical affection between mothers and babies, sexual lovers (after an initial "
dopamine" or pleasure chemical infatuation) or even platonic friends.
God in His essence does not have a body or any materiality, He is pure spirit. So no hormones or chemicals.
Likewise, human love involves not just hormomal-driven physical intimacy but
emotional intimacy as well. God on the other hand is "
impassible": He has no emotions. This is known as the doctrine of divine aseity.
This doesn't mean that God does not "
love" us all - indeed He wills, positively, the good of everyone and all things that He has created.
As the Book of Wisdom, in the Catholic Old Testament, informs us:
For you love all things that are
and loathe nothing that you have made; for you would not fashion what you hate.
25How could a thing remain, unless you willed it; or be preserved, had it not been called forth by you?
26But you spare all things, because they are yours,
O Ruler and Lover of souls,
12:1for your imperishable spirit is in all things!
(Wisdom 11:24-26, 12:1)
Christianity, however, nuances this yet again quite considerably by introducing two radical concepts:
(a) that God, whilst one in essence, relates to Himself as three "persons" engaged in eternal relations of origin, whereby God the Father loves Himself in His own Image which is the Son and this bond of love between them spirates as the Holy Spirit
(b) God the Son has incarnated and become a living, breathing, emotional, hormonal and physically intimate (during his lifetime) human being in the person of Jesus Christ
This redefines the playing field for Christians, since the revelation of Jesus as God incarnate comes with the message that God doesn't just "
have" love as an attribute among others such as His mercy and glory (as in Islam and Judaism, arguably) but that He actually
is love Itself in his very essence and being through the intimate, eternal relations of the Three Divine Persons of the Trinity, the Triune God, one Person of which assumed flesh as a human and "loves" just as a human does in his human nature.
God "
is" love as the First Epistle of John tells us, and He calls us through His incarnate, en-fleshed Son (the 'image' of the Father) to share in this love for the Father through the Son in the the unity of the Holy Spirit, which is the inner life of the one God, His very essence and being.
This divine love has 'flowed' out into creation through the incarnation of that Son, the image of God, who became incarnate
flesh as the Bridegroom to 'invite' the human race to share in the "intimacy" of Father and Son in eternity, because the entire human race is the Bride that the Father has prepared for Jesus the Bridegroom.
"
Beloved, let us love one another, because love is from God; everyone who loves is born of God and knows God. Whoever does not love does not know God, for God is love. God’s love was revealed among us in this way: God sent his only Son into the world so that we might live through him." (
1 John 4:7-9)
Christianity places the 'scandal' of this fully incarnate God - conceived and born of a mother's womb, a God who in his lifetime was seen and touched, kissed and hugged - at the
heart of its understanding of the meaning of existence. As the prologue to the Gospel of John ends: "
No one has ever seen God. It is God the only Son, who is close to the Father’s heart, who has made him known."
This point is rammed home so very beautifully in the Johannine epistle, typically known as 1 John, that accompanies the Gospel and was cut from the same theological cloth (a product of this ancient 'school' or sect of first century Jewish Christianity, founded by the anonymous Beloved Disciple of Jesus ("
the disciple whom Jesus loved" and had reclining at his breast at the Last Supper)):
Bible Gateway passage: 1 John 1 - New Revised Standard Version
We declare to you what was from the beginning, what we have heard, what we have seen with our eyes, what we have looked at and touched with our hands, concerning the Word of life— 2 this life was revealed, and we have seen it and testify to it, and declare to you the eternal life that was with the Father and was revealed to us— 3 we declare to you what we have seen and heard so that you also may have fellowship with us
Consider the emphatic '
emphasis' placed here in this passage on the
sensuality - full sensuality - of the eyewitnesses (the disciples) first-hand encounter with God made flesh, the Divine Word in male humanly embodied form. Their every sense -
hearing, seeing, touching - did he arouse in them. They are groping for temporal, earthly linguistic categories that can adequately convey the power of this engagement with the Divine-in-flesh.
So, to say the least, "
divine love" and its relationship to a human love like that of a mother for her child, is a complicated thing and heavily shaped by your conception of theism.