What are the similarities between Sufism and Buddhism?

Many people forget that Buddhist missionaries have been active in the Middle East since 200 bce.  Many New Testamnet passages contain the teachings of Lord Buddha but not many know that The Koran also has some things such as the miracle of the splitting of the moon: Chapter 54:1 of the Koran is from a Buddhist Jataka, the Matanga Jataka:

Matanga Jataka

"Excellent! When they ask you where your husband has gone, you must reply, 'He has gone to the Brahma heavens.' If they ask when he will come back, you must say, 'In seven days, he will come, breaking through the disk of the full moon!' Can you do that?"

Surah 54 of the Quran is called “The Moon.” It starts by saying:

The hour drew nigh and the moon did rend asunder
And if they see a miracle they turn aside and say: Transient magic.
And they call (it) a lie, and follow their low desires; and every affair has its appointed term.

Buddhist influence on Sufism:
Throughout the region, there are many indications of cultural borrowing between Buddhism and Islam. For instance, Kazakh Sufis not only believe in rebirth, but also identify reincarnations of past Sufi masters like the Tibetan and Mongol Buddhists do of their teachers. The Sufis build shrines as graves for their masters, circumambulate them and light butter lamps, reminiscent of Buddhists' practice around stupas of deceased masters. Sufi meditation includes recitation of the Islamic equivalent of mantras, often combined with the breathing cycle, as well as visualization of the Prophet and spiritual masters.

Buddhism has the concept of “becoming empty.” in the beautiful heart sutra of Buddhism it says that all forms are empty, and what we think to be empty has form. the concepts, ideas, and images that we hold in our minds have forms. the forms that we see on the outside are empty. the heart must be made empty of all other thoughts apart from the thought of God.
..."thou shalt have no other Gods before me.”-Old Testament. the false idols that we hold in our hearts and minds become false gods that cover the true Self that IS Allah.