Wait so you guys agree that Buddhism and Adwaita-vada are quite similiar? Hahaah last time I said that to an Adwaitin, he had a complete go at me. It was brutal. The debate lasted like 2 weeks, back in the days were I was quite immature...(thought I had to pick a fight with everyone ahha)
Criticism against Gaudapada's doctrine as pseudo Buddhism was already present during the time of Shankara as he makes note of it in his karika-bhashya. The earliest known criticism of Shankara's mayavada as Buddhism comes from Bhaskara and the same criticism was echoed later by Yamunacharya and Ramanujacharya.
However, we have to put this issue in proper perspective. By the time of Gaudapada, there already existed four prominent and distinct sects of Buddhism in India - of which, two are relevant to this discussion.
1. vijnana-vada by the brothers Asanga and Vasubandhu - Consciousness alone is real and everything else is in the mind. That is, the universe is unreal.
2. shunya-vada/madhyamaka by Nagarjuna - Everything is empty by nature.
Gaudapada does three things in his karikas. He accepts the authority of the Veda and accepts the reality of Brahman; his world view resembles that of the vijnana-vadins (karika 2.15, etc) and his dialectics are borrowed from Nagarjuna. To be fair, it is possible that his doctrine did not come from vijnanavada, but from an alternate, unknown source which is neither a Buddhist doctrine or the Upanishads. This may be a possibility because we have the text yoga-vasistha which may be older than Gaudapada and already supports the idea of everything being in the mind.
One of the big arguments is that the nirguna Brahman is essentially the same as Nagarjuna's shunya (which is incorrectly translated as void). Nagarjuna's shunya is not a void, but something that is beyond words; beyond description - which is the same as the Nirguna Brahman as it cannot be described. However, since it is established that the indescribable Nirguna Brahman comes from Yajnavalkya (Brhadaranyka), who lived long before Nagarjuna, it is not true that Advaitins copied the concept of Nirguna Brahman from Nagarjuna. But it should also be noted that the same Upanishads are interpreted very differently by other schools of Vedanta (without a Nirguna Brahman).
There is no denying that the ideas are strikingly similar - that is, there is a strong case to make for Advaita (Ajatavada, specifically) being crypto Buddhism. Similarly, I would like to note that tattva-vada and vishishtadvaita are very similar to the older bedha-abedha doctrine of Bhaskara.