Also, do they cite one another?
The meaning of the Rigveda and Avesta is a matter of much dispute to this day which is why you will often find wildly different meanings given to words and expressions, where usually one would be drawn from living Indian tradition and another from the discourse of European scholars drawing on cognates in Ancient Latin, Ancient Greek, Arabic and other well-studied languages. Since there was much dispute between the advocates of the two different approaches nowadays neither is considered completely satisfying and translators will commonly pick different ways to translate the same phrase in different contexts (unless, of course, the translation is out of date or has been done by a still partisan minority).
Sources:
Ankeev N.P., Upanišady, Moscow: Nauka, 1969.
Rak I.V., Zoroastrijskaja Mifologija, Moscow: Letnij Sad, 1998.
Edit: As to what concerns citations, some of the views espoused by Zarathustrian scriptures can be read as critical of a hypothetical Vedic Religion. Zarathustra was opposed to the burning of the dead and it is emphasized it is your thoughts, words and deeds that matter in afterlife (as opposed, supposedly, to caste. There is explicit mention of an evil prince and a pious peasant). The angels in Zoroastrianism are referred to by the same word as devils are in Hinduism (ahura/ashura) and vice versa (daeva/deva).