This happened recently during a private screening of Sivaji - The BOSS. Rajnikanth invited Big B for the screening. Previously Rajni was invited for IIFA awards by IIFA ambassador Amitabh Bachan himself, but Rajni couldn't make it due to Sivaji's release. In spite of recent comparisons between the two, they share a mutual admiration for each other!
Amitabh is an Emperor and I'm the King probably...
More on this:
Rajni Vs Amitabh