At the moment, it is too early to say if Binance.US will employ security technologies from the global Binance platform which are usually described as being solid, despite a major hack this platform suffered in May 2019. Yet, the platform also responded to this incident in a generally well-received and timely manner.
As of Wednesday 9 AM (GMT+3) November 10th, here are the prices of the top 10 cryptocurrencies:

This is just one example, but it definitely highlights the difference between trading on Binance and Binance.US. Although small traders won't make much of an impact on either exchange, all else being equal, most traders would prefer to trade against the larger book, rather than the smaller one.
The horizontal axis shows the time; relationships positioned towards the leftmost area of a diagram occurred at the start of the data interval considered, and those at the rightmost end occurred at the end of the data interval considered. The vertical axis shows the period; lower period bands (higher frequencies) are shown near the top and higher bands (lower frequencies) are near the bottom. Lower bands would be of interest to investors with short term horizons, whereas higher bands would be of interest to investors with longer term horizons.