Bharatanatyam and kathak are pretty similar yet very different. More than differences between originating respectively from south and the north, the dances are distimguishable by how the kathak has limited or zero hip movements, and in the musical instruments used. The music and its beats are also different.
Bharatanatyam tells the tales of Shiva while kathak speaks of the romance between Radha and Krishna. Kathak is the dance of the historical times when it was brought from the Hindu temples to the Muslim courts of the Mughal Empire. These dances share slightly similar characteristics in the foot percussion to the flamenco, likely from influences along the ancient Persian trade routes.
Attended 'Nritya Rang: Expressions of Kathak' at Esplanade Theatre Studio. Such a treat to watch kathak soloist Ponnamma Devaiah perform pieces in the styles of Jaipiur and Lucknow. She's been based in Singapore for a few years now. There're three main schools of kathak today- Lucknow, Jaipur and Benares. I'm not versed enough to discern the differences between them; neither am I so familiar with the stories of Radha and Krishna. I simply enjoyed the dance and imagined the stories. It was a very lovely evening with the friends.