A video mashup of the two hits has gained almost 400,000 views in just over two days.
YouTube user Robin Skouteris created the video, which splices together visual elements from both videos and perfectly marries the songs in the audio.
The video has gained over 400,000 views on video sharing site YouTube since it was posted on the 4th of October.
The two singers have gained the attention of social networking sites since Cyrus' mocked O'Connor's mental health issues following an open letter by O'Connor to the star.
The exhanges began when Cyrus claimed her 'Wrecking Ball' video was like O'Connor's 'Nothing Compares To You' but the "most modern version".
You can see more from the creator here.