I shall go on and attempt to evaluate China's and US's progress in attaining such "qualities".
For the equal opportunities for gender part, China has made significant progress over the past few decades, girls have been allowed into classrooms, the workplace has growing numbers of female office workers. However, we will have to admit the female population most of the time do not rise to the higher ranks in the corporations,they tend to remain as secretaries, low-rank clerks, as well as dwell in the nursing and education professions. However, girls in China tend to receive more equal treatment when they are students rather than at their workplaces, showing how gender stereotypes set in at adult age when realistic ideals set in on them. Meanwhile at the United States, the workplace demographics is quite similar to China's, however compared to China, not much progress has been made in the past decade as people seemed to be relatively satisfied with the status quo and that they deem the status quo as gender equality. Although feminist movements are still rallied form time to time, it has seemed to settle down a bit.
For the racial equality part, China is trying hard to open up the Western regions as well as the Central regions of China where most of the other ethnics reside and where people are much much poorer compared to the Hans living at the coastal areas. Well, the western regions' GDP has surged in the past few years but starking contrast in the lifestyles between the Hans and the minorities can still be seen. Thus, more work can still be done. It is also quite similar in the States, as the African-Americans and the Hispanics tend to reside at the Southern states. There is no equal mixing of the different races, resulting in inevitable misunderstanding and unfair treatment as there would be different jobs and different opportunities at different states. Thus, both countries can work more on spreading out the racial demographics.
For the meritocracy part, I would say US is quite far ahead of China. China's central government still has the "habit" of passing the roles from one generation to the another. The Central government 's children tend to have a easier education path then the other kids. The kids of the bosses of the corporations under the government also tend to go to better schools. The contrast in school fees between an independent school as well as a public school is appalling, such that poorer students are denied from entering such schools. At the workplace, results no longer play a huge role as connections beat everything. If you know the boss, you will be most likely hired. The United States have provided much subsidies into education to ensure equal opportunities for all the kids. Compared to China, US kids tend to receive equal education everywhere whereas China kids that reside in villages barely touch on English. In the workplace of US, results tend to be taken into consideration more seriously and less prejudice given to people from poorer background.
For the corruption and crime rates part, China definitely beats United States hand-down in terms of who has a higher number of corruption cases be it hidden or revealed. It would not be a sweeping statement to say that every country has at least a corrupted official. However, as China's bureaucracy is dominated by formal War-heroes or their descendants, their habit of dominating whatever they have is still in their blood and they tend to embezzle funds behind the opaque walls they hide behind. Coffee money has also become a way of life when it comes to delaing with the high ranking officials. Some may argue that the current officials are now educated people with highly recognised degrees or even doctorates, however, their bank accounts and how they send their children to highly acclaimed universities, using the money in their wallet gives us some hint on how and where they get the money from. China's crime rate is definitely high but they tend to be carried out at the coastal cities as the poor mug the rich, due to the income disparity across the country. China also has many food safety issues and etc. Significant progress has not been made in terms of resolving crime rates but the indiction of Bo Xilai could be the turning point for China's corruption problem. The United States has less significant corruption problem, as compared to China, as they have a tidier Cabinet as well as better structured agencies for corruption prevention.Nevertheless, corruption cases can still be reduced. The Gun laws in Texas can also be a turning point for the United States Crimes Resolution as though the government believes that guns are tools for the safety of the citizens but nevertheless, it is undeniable the chief tool of mischif and crime, posing as a safety threat for US citizens. Thus, progress has been made, as the case of gun laws is now currently widely debated and brought into sight.
For the policies and infrastructure, we will have to take into consideration that the huge disparity in structures in China has made it relatively impossible to compare as a country. Shanghai is a world class city but provinces like Yun'nan does not have cities that can stand up to New York. China has made significant progress in terms of infrastructure in the city as the world's fastest train network has been built etc. United States meanwhile falls back in terms of progress as the Financial Crisis is still bugging them and other matters like healthcare remains to bug them. However, China's policies tend to be less tantalising to the people in China as they tend to be misguided and less helpful to bigger population due to the small number of people in the Central government making the decision, being unable to take into account of several minor details which makes policies less fair and helpful.
For the environment protection part, US is definitely way ahead of China, with regards to the Beijing Haze PSI issue, as well as to many of the concerning issues that China has to provide. Although US has not exactly spearheaded any environmentally friendly developments, it has met several of the world requirements, Kyoto Protocol (without ratifying it) and etc. as well as continue to build sustainable energy sources while attempting to invoke less harm to mother nature, as they continue to provide harsh bans on illegal logging etc. China may not be doing well but huge progress has been made. Government has come up with policies that reduce carbon emissions from factories as well as to stop water pollution. The impact of the policies has been felt, though it still has a long way to go before China attains similar results as the United States. We have to understand that it is hard for China to actually realise their economic targets as a developing country and to be environmentally friendly at the same time, as US was also once a major "pollutant". Nonetheless, it has made significant progress despite major rain-forest deforestation and drying up of plains, it is still progressing and will eventually reach there if harsher measures and larger personnel are deployed to ensure they are being adhered to.
In conclusion, both countries have made progress in all the different segments but they are still far from reaching the destination---a supposed ideal society. Nevertheless, both countries have made desirable progress and deserves recognition for their efforts.