While local (Wuhan) and provincial (Hubei) government officials dropped the ball (though it's not clear if they needed permission from national officials to go public about the virus and didn't receive that permission), as they've known about the infections since early December, once the national government started their response, I have to say they've done a pretty good job.
Quarantining cities that total ~50mm people is no easy feat, nor a decision taken lightly. But this, along with incredibly high levels of awareness in all of China, could lead to the virus burning out relatively quickly. Because of the longish incubation period, and all the traveling for Chinese lunar new year, we won't know how high the transmissions that have already taken place will go. But given what I'm seeing, I think the new infections starting from this weekend will be very low (barring significant mutation).
A virus is like a fire - it needs a continual supply of fresh hosts. And the Chinese response, which is unprecedented in its scale or scope, is going to dramatically decrease that supply.
The medical community is certainly way more prepared than they were during SARS. Back then, many medical personnel were infected because they weren't routinely asking if the patient had traveled recently and as a result, not using PPE. That has totally changed. And outside China, seems all the countries are very quick to identify the virus and quarantine patients, and trace contacts.
Overall, I'd have to rate the current Chinese and global response an A. One criticism is how many countries were slow to halt, or never halted, flights from Hubei. And only a couple of countries are halting all incoming flights from China. Although given the lack of evidence thus far of transmission outside China (in fact, I haven't seen much in the way of evidence of transmission outside Hubei), this kind of extreme measure, essentially quarantining the entire country, may be overkill.
