Atheism is a greater sin than shirk
Question

                Which is a greater sin: Atheism or polytheism?.
Praise be to Allah.Atheism, in 
    modern terminology, means denying the Creator altogether, denying that He 
    exists and not acknowledging Him, may He be glorified and exalted. The 
    universe and everything in it, according to their claims, came about purely 
    by chance. This is a strange view which is contrary to sound human nature, 
    reason and logic, and is contrary to simple logic and indisputable facts.  
As for shirk 
    (polytheism or associating others with Allah), it implies belief in Allah, 
    may He be glorified and exalted, and affirmation of Him, but it also 
    includes belief in a partner to Allah in His creation, who creates or grants 
    provision or brings benefit or wards off harm. This is shirk al-ruboobiyyah 
    (ascribing partners to Allah in His Lordship). Or it means belief in a 
    partner to whom some kind of worship is devoted as an act of love and 
    veneration, as it is devoted to that person or thing as it should to devoted 
    to Allah, may He be glorified and exalted. This is shirk al-‘ibaadah 
    (associating others with Allah in worship). By studying these two 
    deviations, we may see that each of them involves sin and evil which tells 
    us that they are bad and we see how Allah described them as being like dumb 
    animals. 
Allah says 
    (interpretation of the meaning):
“Have you 
    (O Muhammad صلى الله عليه وسلم) seen him 
    who has taken as his ilaah (god) his own vain desire? Would you then be a 
    Wakeel (a disposer of his affairs or a watcher) over him?
44. Or do 
    you think that most of them hear or understand? They are only like cattle
    nay, 
    they are even farther astray from the Path (i.e. even worse than cattle)”

    [al-Furqaan 25:43-44] 
“And 
    surely, We have created many of the jinn and mankind for Hell. They have 
    hearts wherewith they understand not, and they have eyes wherewith they see 
    not, and they have ears wherewith they hear not (the truth). They are like 
    cattle, nay even more astray; those! They are the heedless ones”

    [al-A’raaf 7:179].

    Nevertheless, the atheist who denies the existence of Allah and rejects His 
    Messengers and disbelieves in the Last Day, is in a greater state of kufr 
    and his beliefs are more reprehensible than the one who believes in Allah 
    and the Hereafter, but he associates something of His creation with Him. The 
    former is stubborn and arrogant to an extent that can not be imagined or 
    accepted by sound human nature. Such a person would transgress every sacred 
    limit and fall into every sin; his worldview would be distorted to an 
    inconceivable level. Yet many scholars who discussed the issue of atheism 
    doubted that this has deep roots in the hearts of the atheists, and they 
    affirmed that the atheist is only professing atheism outwardly; deep down he 
    believes in one God. 
Shaykh 
    al-Islam Ibn Taymiyah said a great deal which indicates that this group of 
    atheists who deny and reject the existence of God are in a worse state of 
    kufr than the mushrikeen who associate partners with Him. We will quote a 
    little of what we have come across: 
He (may 
    Allah have mercy on him) said: Kufr (disbelief) means not believing in Allah 
    and His Messengers, whether it involves rejecting or it consists of doubt 
    and uncertainty about the issue or ignoring the issue altogether, out of 
    envy or arrogance or following whims and desires that divert a person from 
    following the Message. However, the kaafir who rejects and disbelieves is in 
    a state of greater kufr, although the one who rejects and denies out of 
    envy, even though he believes that the Messengers brought the message of 
    truth, is also in a state of kufr. End quote. 
Majmoo’ 
    al-Fataawa, 17/291 
He also 
    said: 
The one who 
    denies the Hereafter but believes that this universe is created is described 
    by Allah as a kaafir. The one who denies it and says that this universe 
    existed from eternity is a worse kaafir in the sight of Allah, may He be 
    exalted. End quote. 
Majmoo’ 
    al-Fataawa, 17/291 
He said (may 
    Allah have mercy on him) refuting those who deny the Divine attributes: 
(Denying the 
    Divine attributes) implies complete denial which reaches the point that 
    says: There is nothing that must exist and cannot have not existed. If he 
    believes that and says: I do not affirm either existence or non-existence, 
    then the answer to that is: Suppose you state that verbally and in your 
    heart you do not believe either of the two; rather you turn away from 
    knowing Allah and worshipping and remembering Him, so you never remember 
    Him, worship Him, call upon Him, put your hope in Him or fear Him; (in that 
    case) your denial of Him is worse than that of Iblees who (at least) 
    acknowledged Him. End quote. 
Majmoo’ 
    al-Fataawa, 5/356. 
And he (may 
    Allah have mercy on him) said: 
The arrogant 
    one is the one who does not acknowledge Allah outwardly, like Pharaoh. He is 
    in a worse state of kufr than them (meaning the mushrik Arabs). Iblees, who 
    enjoins all of that and loves it and is too arrogant to worship his Lord and 
    obey him, is in a worse state of kufr than them (the mushrikeen), even 
    though he was aware of the existence and might of Allah, just as Pharaoh was 
    also aware of the existence of Allah. End quote. 
Majmoo’ 
    al-Fataawa, 7/633 
He also 
    said:  
The view of 
    the philosophers -- those who say that the universe is eternal and that it 
    is dependent on that which inevitably must exist -- came from the minds and 
    hearts of those who worshipped heavenly bodies and made images of them on 
    Earth, such as Aristotle and his followers. This view is worse kufr and is 
    more misguided than that of the Arab mushrikeen who believed that Allah 
    created the heavens and the earth and everything between them in six days by 
    His will and power, but they attribute falsely without knowledge sons and 
    daughters to Him (cf. al-An’am 6:100) and joined others in worship with 
    Allaah, for which He had sent no authority (cf. Aal ‘Imraan 3:151). 
    Similarly, the permissive people, who do not believe in any command or 
    prohibition at all and refer to the Divine will and decree as an excuse for 
    their evil deeds, are worse off than the Jews, Christians and Arab 
    mushrikeen, because even though the latter are kaafirs, they still believe 
    in some kind of command and prohibition, and the promise and warning (i.e., 
    the Hereafter), but they had partners with Allaah (false gods) who 
    instituted for them a religion which Allaah had not ordained (cf. al-Shoora 
    42:21), unlike the permissive people who ignore all laws altogether. They 
    are only pleased with whatever suits their whims and desires, and they get 
    angry on the basis of their whims and desires; they do not get pleased for 
    the sake of Allah, or angry for the sake of Allah, or love for the sake of 
    Allah, or hate for the sake of Allah; they do not enjoin that which Allah 
    has enjoined and they do not forbid that which Allah has forbidden, unless 
    that suits their whims and desires, in which case they do it for that 
    purpose and not as an act of obedience to their Lord. Hence they do not 
    denounce what takes place of kufr, evil doing and sin unless it goes against 
    their whims and desires, in which case they will denounce it, prompted by 
    their devilish nature and not prompted by sharee’ah and love of Allah. Hence 
    the devils plunge them deeper into error, and they never stop short (cf. 
    al-A’raaf 7:202), and the devils may show themselves to them and address 
    them and help them with some of their whims and desires, as the devils used 
    to do with the mushrikeen who worshipped idols. End quote. 
Majmoo’ 
    al-Fataawa, 8/457-458. 
Shaykh Ibn 
    Baaz (may Allah be pleased with him) said: It is shirk to worship something 
    other than Allah completely; that may be called shirk or kufr. Whoever turns 
    away from Allah altogether and directs his worship to something other than 
    Allah, such as trees, rocks, idols, the jinn or some of the dead, those whom 
    they call awliya’ (“saints”), worshipping them or praying to them or fasting 
    for them, and forgetting Allah altogether -- and this is the worst kind of 
    kufr and shirk. We ask Allah to keep us safe and sound. 
The same 
    applies to denying the existence of Allah and saying that there is no God 
    and life is material, like the Communists and atheists who deny the 
    existence of Allah. These are the worst disbelievers among mankind, the most 
    astray, the most involved in shirk and the most misguided. We ask Allah to 
    keep us safe and sound. End quote. 
Majmoo’ 
    Fataawa Ibn Baaz, 4/32-33 
He also said 
    (may Allah have mercy on him): 
Meat 
    slaughtered by Communists is haraam and is like the meat of the Magians and 
    idol worshippers; in fact their meat is even more haraam, because their 
    degree of kufr is greater due to their atheism and denial of the Creator 
    (may He be glorified and exalted) and His Messenger, and other kinds of 
    kufr. End quote. 
Majmoo’ Fataawa Ibn Baaz, 23/30 
And Allah knows best.