Both dramas are based on the same history surrounding Hong Taiji and Da Yu'er. The characters in The Promise of Chang'an are counterparts of historical figures in Qing Dynasty during the respectful time period:
He Lan Mingyu - Da Yu'er
Xiao Chengxu - Dorgon
Xiao Chengru - Hong Taiji
He Lan Wanyin - Ha Lan Zhu
The only significant difference is the Promise of Chang'an is set in a fictitious dynasty rather than the Qing Dynasty due to censorship.
It's also ironic that Han Dong (who played Dorgon in 'In love with Power') plays Xiao Chengrui, Hong Taiji's counterpart.