What we call "Western Culture" is mainly based on Christianity, Greek and Roman culture, as well as to a tiny amount on other pre-christian European cultures. From the late 15th century on until the early 20th century
Western Europe (inclusivly and even INITIALLY
IBERIA!!!!
) rapidly started being the military and cultural dominant force in the world, technologically overtook the Muslim countries first, colonized the Americas and destroyed American civilizations, enslaved Africans, colonized India, large parts of East Asia, the Pacific and Australia. It invented most of recent technologies in engineering, chemistry and medicine, and was the first on the moon. Even after Western Europe and USA withdraw from their colonies, it remained the cultural and moral power in the world, with everyone copying Western life style, consuming their products, wearing their clothes, like suits etc... Politically it succeded over the Soviet Countries and Eastern Bloc. The UN-Charta is based on Western values. The economy of North America and EU combined is still with distance the strongest in the world. So are their armies, even if European armies lack the power they once had.
So it is only natural that the Western World feels superior over the rest of the world. A long time it was suggested that "Western Thinking", enlightenment or what so ever was the reason for Western superiority. Say: if you think like a Westener, progress and power will come on it's own.
human rights, freedom of speech, democracy, liberty, christianity (OR alternatively atheism), equality = military power, technological progress, affluence, wealth, peace on the long run etc... [even if the one or other contradicts itself]
Ironically, besides the many Western European politicians, media, development workers and philanthropists who hold up the "White Man's Burden" to teach it's values to bring progress to the world, not just a few people from outside the Western World also believed in this logic, and tried to copy Western life-style, tried and subsequently pretended to "think Western", in order to become successful in life. And not just a few failed with this tactic, partly because the ideas behind these values were not understood, partly because the causality between values and alleged progress was simply wrong. But neither people from the West and non-West tried to give up with this work and questioned this logic.
Now comes the part at which China enters the stage! Within a very short time and for the first time in centuries the Western World gets a serious opponent who is completely of non-European descent. An opponent on political, economical, technological and military bases. An opponent who is obviously not interested in Western values, who doesn't need them AND it very successful without them. Even though Western countries were taught that this can't be possible... And not only that: With the proof that success is not necessary with Western values anymore, also other non-Western countries of the world are starting to turn their heads away from EU and North America, heading to China. A country that doesn't bases it's business on conditions like human rights, democracy, freedom of press etc..., which even makes life in many points much easier. Subsequently, also the relation between the West and other non-Western countries than China will presumably change.
Now, that the Western World and it's values are questioned, in the following years USA and Europe have to re-think about their position in the world, but are currently still a little perplexed how to deal with this problem.
I don't think that Americans and Europeans see China any differently from each other. We consider Chinese in their culture as very different from ours, don't know yet how to manage and cope with the potential chances and dangers, and treat them with caution and respect.