Khwaja Mere Khwaja in hindi is definitely the original and the tamil version is the dubbed version as clearly comes out after this A R Rahman’s interview::

‘I composed it just for me to listen to’

And then one fine day, in 2005, he decided to compose the song. “I composed it just for me to listen to,” Rahman continues. “When Ashutosh told me the story of Jodhaa Akbar and about the influences of Sufis and Khwaja sahib, I told him of the song I had composed. He asked me to play it to him and he remarked immediately, ‘I love it, I want to use it in my film.’
“So I told him only if you can give him (Khwaja Chishty) the respect he deserves, he can use it in the film,” Rahman adds.

“He did not change anything of what I composed for the film,” he continues. “We had to use interludes and extra sounds for the new version but the song has been put to great use in the film. The song was originally titled Kashif, for the person who wrote it. He was a very spiritual person as well. Therefore, the song is very spiritual to me.”

In the film, much of the song is pictured on Haidar Ali, who wrote the film’s story and collaborated with Gowariker on the script.

“Ashutosh told me he would use the song in a sequence showing Akbar triumphant,” Rahman continued. “He is married to a Rajput princess and he had made an important political alliance. But he also sees a spiritual light as he watches the singers and dancers. It is accompanied with a Rumistic, Sufi kind of dance.”

Appreciate inputs from all and sundry.

(Please Note::: For people who don’t know, the hindi movie was released first (15/2/2008) (and it was decided only later that the tamil/telegu dubbed versions won’t be released until 6th March 2008)