Hi Gyan,
You are right about the presence of two Allahabad Universities. So the first one is a central university and it is way more famous and reputed. It was established in 1887.
The Allahabad State University was established in 2016 by the Uttar Pradesh Government. The university is still in its infancy stage and is thus not proven yet to be as good. It is also a decent option though since it a state govt university like GGSIPU and the rest.
All the best.
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