Old Avestan and Vedic Sanskrit were so close to each other that they could be considered as dialects of the same language rather than separate languages. Therefore, they would have been mutually intelligible.

The main difference between them was in pronunciations. Some verses from the oldest portions of Avesta can be read as Vedic Sanskrit just by accounting for differences in pronunciations.

An example of how Old Avestan can be read as Vedic Sanskrit is given by Brunnhofer [1] with this passage from Yasna 10.8:

Old Avestan

yo yatha puthrem taurunem
haomem vandaeta mashyô:
frâ âbyô tanubyô
haomô vishaite baeçazâi

Vedic Sanskrit equivalent

yó yáthâ putrám tárunam
sómam vandeta mártyah:
prá âbhyas tanû́bhyah
sómo viçate bheshajấya

Vedic Sanskrit in Devanagari

यो यथा पुत्रम् तरुणम्
सोमम् वन्देत मर्त्यः
प्र आभ्यस् तनूभ्यः
सोमो विशते भेषजाय

Translation [2]:

To (that) man who praises Haoma like (his) young son, Haoma enters into his body for giving health.

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[1] Dr. Hermann Brunnhofer: History of the Aryans

[2] Prof. Ervad M.F. Kanga: Khordeh Avestā