That is a hard question to objectively answer, since the criteria from any person would mostly vary based on their own preferences.  However, if it were possible to narrow the criteria to only those characteristics that can be quantitatively measured (which is almost impossible as well), the following is list of characteristics that I would use to measure a nation's greatness.  Each nation would be ranked by each criterion to each other moderated by country size and level of overall development.


Justice/Personal Liberties
1. Rule of law
2. Due process
3. Unalienable human rights


Government
1. Inflation control
2. Unemployment/Underemployment control
3. Interest rate stability
4. Budget deficits
5. National debt
6. Business regulations


Economics
1. Equal employment opportunity
2. Equitable distribution of wealth
3. GDP
4. Poverty


Education
1. Equal educational opportunity
2. Literacy
3. Math/Science proficiency


Health and Human Services
1. Equal access to healthcare
2. Government assistance for the needy/elderly/disabled/etc. (i.e., food clothing, shelter, healthcare)


Public Safety
1. Crime rates
2. Police abuses/brutality
3. Incarcerations


National Security
1. Terrorist attacks
2. Foreign invasions from abroad
3. Foreign wars participated (direct/indirect/proxy)


The list above is not meant to be an exhaustive list, as there are many other items that could be added to the list.  As to the question which country is the greatest today, even with the list I compiled is still trivial.  Personally, I think Singapore is the greatest country to live in based on the above criteria.

When measuring both US and China to my list, the only area I see the US having a great advantage is with justice/personal liberties and marginal edge in health and human services.  China does a slightly better job in running their country, great job in maintaining a more equitable economy, and excellent education.  China's public safety and national security are only better than the US because US scores lower on the metrics that compile both items.

Once again, this list is very subjective on my part and I know opinions will differ.

I was not sure what your answer was going to be. But I didn’t expect Singapore. So would you consider moving there if/when you get fed up with the US?

Singapore is a country I would not consider living in myself. But that is a personal choice.

A lot of that criteria is socialist / govt control. There's little room for free market or freedom for that matter in that list. Keynesian economics comes to my mind.

Since measuring the "free market" and the concept of "freedom" itself would be too subjective, I thought it more appropriate to gauge those attributes by analyzing the amount of business regulations for the "free market" and the level of rule of law, due process, and human rights; as a proxy for "freedom".

BTW, I am impressed by your mention of Keynes, as most Keynesian economists would be very familiar of the many attributes I listed.

Do you consider yourself a Keynesian?

I used to; but am more pragmatic in my economic beliefs than in my youth.

My undergrad is in BA but I got that decades ago. I don't remember much details about Keynesian economics but my first professor was very much a free market believer. The main idea I got from Keynesian is govt. control over the market i.e. prime rate manipulation etc. I'd have to read up on it to freshen my memory.
I know that our local leaders visited Singapore in hope of instilling some of their housing principles but I hope they realize that our forms of govt. are very different. All I know is that Dem / liberal controlled cities such as San Fran have gone downhill in terms of homelessness.

Change my mind.