Shirk

In theory, atheism is different from shirk.

In practice, it is often the same. Atheism usually leads to replacing theism with some sort of -ism such as nationalism, tribalism, communism, scienceism, secularism, etc, and this results in something else being treated as a partner of God (for instance, as something to appeal to in a time of need, as the height of perfection to try to attain, as what you live your life for). 

It is hard to say which is worse. On a social level, both atheism and degenerate polytheism cause harm. Places where there has been a push towards atheism often have a lot of problems such as totalitarianism, dictatorship, or corruption, as well as a sense of nihilsm or despair. Atheism as a state ideology has not brought happiness, justice, or a healthy and sustainable prosperity anywhere. 

Similarly, although secularism is not inherently atheist, secular social service organizations and interventions can provide functional help, but generally don't have the same ability to spread compassion and build community that religious institutions often do. That is, they can take care of some material problems in society, such as providing housing services, but they largely have not yet been able to deal with the human aspect of building community, bringing peace in a neighbourhood, encouraging love and forgiveness, uplifting people, and eradicating misery.

On the other hand, historically, degenerate polytheism has also tended to reinforce social injustice - for instance, reinforcing unhealthy taboos, wastage of money for unnecessary religious ceremonies or priesthoods while people are in poverty, injustice towards women, superstition, or privileging the elite. 

In fact, one can say that some of the problems in the Muslim world are due to various forms of lesser shirk - for instance, people worshipping traditions or national/tribal identity instead of God. 

On a personal and spiritual level, it really depends. I think that the biggest personal challenge of atheism is the loss of meaning and greater purpose in life. Some atheists also do unethical things to other people because they don't see anything wrong with it. (Yes, you do not need to be a theist to be ethical, but, statistically speaking, it seems to help.)

Of course people who are atheists may have other life purposes, for instance, a dedication to family or the arts; but, even in those cases, something greater than themselves is taking the place of God as a focal point.

Today, atheism is sometimes confused with lack of adherence to organized religion. However, there is an increasing number of people who do not feel fulfilled by organized religion and are unaffiliated, but who do believe in things like heaven or life after death.

And, atheists come in all types. Some are seekers and just haven't been sold on theism or have been put off by some ways that theism has been co-opted (for instance, how Fox News in the US treats Jesus these days), or else had bad experiences with organized religion. In fact I have met some rather spiritually minded atheists.

Some people are just occupied with other things in life.

And then there are some atheists who are genuinely evil and end up using atheism as a front for something worse, such as dictatorship, or starting a cult (obviously, non-theistic cults). But, again, one could classify that as a form of shirk, in the same way that the Pharaoh in the Qur'an deified himself and was not merely an atheist.

So, basically, it's not easy to answer which is worse, atheism or shirk, except that I would go back to what I said in the beginning; and that is, that they tend to go together. 

In any case, the Qur'an addresses both atheism and shirk with the main message that God exists and is present and involved in our lives, that the universe is meaningful, that our existences are meaningful, that we are part of a broader picture, and that theism is part of the road to success.