I think the first one is more likely, but I don't think they will have access to hundreds. I'm gearing more towards like what Huobi did; with Huobi Global having the hundreds of cryptocurrencies, while Huobi(US) only has access to like more or less 20.
It's due to SEC of USA categorizing most of the crypto as securities and having a different set of regulations that is difficult for a crypto exchange to fulfill. Binance US would also be in full compliance with SEC and consist of few number of crypto but most probably have an option of fiat deposit and withdrawal.
They only transfer technology and the way of doing business and all the tokens listed will be subject to US regulations. The most important thing is still the business strategy. But with Binance's reputation I think that is the advantage.