Beijing and Xi'an
 

10 days to split between these two cities. How would you divide your time?

Seven Beijing, 3 Xi'an.

What Marija said. Note that you can take the night train between the two, saving daylight time. For info on train travel in China, see seat61.com

This is plenty of time and there is not even need to train overnight to save time. You should spend of your time in Beijing and can stretch Xi'An to 3 days if you go to Huashan. You can also do Beijing in 5 days and stop somewhere between the 2 cities, such as in Pingyao.

Thank you!