A Step Into The Past (2001)

Both main characters travel back through time.

Both characters travel back though time.

Both include modern person, time travelling back to the ancient times, however this dynasty is much closer to modern times.

Both revolve around time travel and love. Both takes places in the Warring States Period, one in Japan (Ashi Girl) and other in China (A Step Into The Past).

Another adaptation of the same novel.

Both revolve around wandering martial artists who learn some powerful martial arts from some master and end up becoming renown. Both main characters dont rely solely on their martial arts but also on their cunning and careful planning. A Step Into the Past would be a casual recommendation for wuxia fans that have already seen all the better shows like Laughing in The Wind. Both are historicals but A Step Into the Past begins in "modern time".

Similar story-line: The hero(ine) travels into the past, and than stuck there...
In both you can find: timeless love, introduction of modern thinking and devices and funny moments.

Both shows are about male leads who time travel to the past, befriend royals and start impacting the past using their modern knowledge.

in both dramas main lead travels back to past
where legend of ace is more comical version and main lead is funny