As far as I know, Zoroastrian is the closest among all to the Vedic religion.
There are many similarities like:
Both have fire and fire rituals as its core.
Deities like Soma, Mitra, Varuna etc are in both faiths.
Avestan resembles vedic to an extent.
Both have similar customs of sacred thread.
It should be noted that "asura" is not "demon" which is in many later day Hindu texts like Puranas. Many vedic deities are referred to as "asura" in the Vedas Eg: Mitra, Varuna, Indra etc.
In the Purānas and other of the later writings of the Hindus, and also in the popular mind, the Asuras are powerful evil beings; in translations the word is represented by such terms as demons, giants, etc. As the Asuras * were the gods, the asuras were not-gods, and therefore the enemies or opponents of the gods. In the Vedas the name asura is applied more frequently to the gods themselves than to their enemies, whilst it is also used very much in the same manner as in the later writings. In the Rig-Veda, Varuna is accosted as follows: "King Varuna has made a highway for the sun to go over. O thou wise asura and king, loosen our sins!" Again: "The all-knowing asura established the heavens, and fixed the limits of the earth. He sat as the supreme ruler of all worlds. These are the works of Varuna." "Asura stands for the Supreme Spirit," in another verse, and "also as an appellative for Prajāpati or creation's lord." † Again and again Varuna alone, and also in conjunction with Mitra, is called an asura. "All the Vedic gods have shared the same title, not excepting even goddesses."
"Varuna was the all-knowing asura, Prajāpati the Supreme Being; Indra, the Maruts, Tvastri, Mitra, Rudra, Agni, Vāyu, Pushan, Savitri, Parjanya, the sacrificial priests, were all asuras. In fine, Deva (god) and asura were synonymous expressions in a multitude of texts." *
On the other hand, in the Rig-Veda, Indra is the destroyer of asuras. "The same Veda which speaks of the asuras as celestial beings supplies its readers also with the Mantras, by means of which devas overcame asuras. The texts which are condemnatory of the suras as impure and ungodly are far less in number than those which recognize the term as applicable to gods and priests." Dr. Banerjea, in the most interesting and ingenious article from which the above extracts are made, suggests a means of reconciling these contradictory uses of the word "asura." Before the Indo-Aryans arrived in India, they had lived in close proximity to the Persians, the original worshipers of fire. "What could be more natural," he asks, "than that the Asura-Pracheta, or Asura-Viswaveda of the one branch, was but the translation of the Ahura-Mazda (the Wise Lord, according to the 'Zend-Avesta') of the other branch; and that the word 'Ahura,' which the one used in a divine sense, would become a household word in the other branch, in the same sense?" the word "Ahura" being changed into "Asura," in a way common to many other words. He then goes on to say, that as "Assur" was the term used in Assyria for the Supreme Lord, and the Assyrians were for some time the rulers of the Persians, it was natural that this word should find its way into Persia; the only change being this, that the Persians added