Both have characters travelling from a past Japan to the future. In both the ancient characters try to adapt and even look for romance in modern time. They largely keep their old habits but learn a bit about the modern world. The difference would be that Hikaru Genji is a fictional Heian-period character and Senka is supposed to be a real Edo-period woman.
In one drama someone travels from the past to the present (EdoMoiselle) and in the other from the present to the past (Nobunaga). In both dramas, the character knows nothing about the era (s)he is in and has to learn things and adapt to that period. Besides, in both dramas the character uses his/her wisdom from another era to help the people around him/her.
