Neither of them will do so anytime soon, nor  .  . . . ever.

The notion of Bitcoin stands in fundamental contradistinction to the idea of a centralised nation-state. So, as long as that entity exists, there's no space in it's Venn diagram for any non-state virtual currency.

Well, right now the ownership of Bitcoin is not 'illegal' in both countries, US and China.

If you mean the full implemention similar to the national currency, I think it's very unlikely in both countries in the near future. In the US Bitcoin is already very popular, but I think in the government are too many sockpuppets of wallstreet and most of them would lose a part of their power if Bitcoin gets stronger. In addition, the US would do nothing that would endanger the dollar's influence in international competition and that would be endangered with Bitcoin. So it will be very important for the USA to keep the dollar as number one. Also big companies like Visa an Mastercard are influencing politicans to stay away from Bitcoin (and maybe pay them) because Bitcoin is their direkt competitor in digital payment.
Many politicians are against Bitcoin, not everyone is positive like John McAfee.  

And it is not much better in China. The communist government has already concluded many measures to limit Bitcoin, such as limiting mining and discouraging people of buying bitcoin. The reason, in my opinion, is that the government is in danger of losing parts of its power in the country. It is still a very communist country, not a liberal.

But I'm sure the people will see the benefits of Bitcoin, no matter which measures the governments takes to prevent it.

I think China will soon be legalizing bitcoin in the future. I realize that there are many bitcoin investors coming from China although this country does not support electronic money. Many factories to exploit bitcoin are built here. From here, I see that the Chinese government may soon be legalizing bitcoin.

I don't understand why so many of you think that China will legalize it. China is the county with a highly censored Internet and a country that has fought Bitcoin since 2013. They  banned banks from doing business with cryptocurrency exchanges, they forced miners out of the country. Do you really believe they'll suddenly change their mind?

i think USA will do legalize bitcoin 1st and china is not good supporter for bitcoin.another thing china is not favourable country for bitcoin so no chance to legalize bitcoin in china.

I tend to believe US will be first and I'll tell why:
* if you read more you'll see that China's "cashless society" thing is closer to a lie than to reality.
* actually the first can be considered Germany, I think. Malta is next? I am not sure if I am accurate here.
* because of Germany, France, UK and then US may follow
* although 180 turns are not unexpected from China, bitcoin exchanges are still not allowed there, right?

This is a very interesting question. The conflict between these giants is growing every day. I heard that bitcoin was prohibited in China, its mining, and with it all cryptography. But in America, Bitcoin was already taxed. And they are trying to master the technology. By this I put on America)))

It won't be China because that is a communist country where they never want the decentralization in anything then how they will allow decentralized bitcoin into their system but they maybe better in new technologies so they will create new currency for themselves or they will just go with NEO.

China is heavily cracking down on crypto's since last year. China's PBoC doesn't want crypto to take off because of its non-regulated and decentralization. So I have no doubt that legalization is not on the horizon. As far as the US though, they're very careful on issuing regulations as they also afraid of bitcoins pseudo-anonymity. Personally though I think US will at least regulate in the future as we have seen positive statement from SEC Chairman Jay Clayton.

America will be the first country to accept Bitcoin because this is a very developed country and Donald Trump is a smart guy, so he will choose the best things to help him achieve his desire. China is a difficult country to open up to investors, and in particular, China has many bans on Bitcoin and Crypto.