Dear Aspirant,
From a ranking perspective both of them are not in the top 200 universities according to the National Institute of Ranking Framework (NIRF).
Allahabad is a central university while Lucknow is a state university. Access to funding is usually more in centrally funded universities. Allahabad’s Dept. of Mathematics is older. They have a faculty of 11 in comparison to 19 at Lucknow. The difference being Lucknow has Astronomy as an additional elective in their department. In terms of published papers by Allahabad’s HOD has more papers.
So taking all these into account we figure Allahabad has a better Mathematics Dept. We will also recommend that you talk to the faculty of each to further understand to take a hand on decision.
Good Luck
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