Which is better among IIIT Allahabad (IT branch) and IIIT Delhi (CSE branch) if fees isn't a consideration?

IIIT Allahabad and IIIT Delhi are both well known brands.

Before making a choice, you must consider these facts-

1. IIIT Allahabad does not have a Home State Quota. At IIITD, 85 % seats are reserved for Delhi students, and only 15% are allotted for OS students.
2. IIITD has better research labs and classrooms. 
3. IIITD campus covers just 25 acres, while IIITA is spread across 100 acres of land.
4. The faculty at IIITD is better. Some of those teachers have graduated from foreign universities like Oxford, Cambridge, etc.
5. Both the colleges have equally good placements. Last year, B.Tech students at IIITA recorded 100% placements with an average package of 30.63 LPA. This year, the average package for IIITD B.Tech students stood at 25.39 LPA, and 98.36% students were successfully placed from B.Tech CSE.

Both these colleges are really good for your CS/IT studies. You can use the above information to choose between the two.