First of all, to clear any misconceptions, IIITH, IIITD and IIITA are not connected in any manner. Out of the three, only IIIT Allahabad is a member of the actual collective known as the IIITs. 

The common public doesn’t know much about these prestigious colleges. Consequently, they aren’t valued as much as the IITs and NITs. Here are the reasons why-

1. All these institutes offer very few branches, which are mostly IT related.
2. They aren’t as old as some of the IITs and NITs. They were set up even after IIT Guwahati, which is the 7th IIT in terms of establishment year.
3. They don’t possess big campuses and a vast infrastructure.

But those who belong to the field of engineering (especially IT), give high ratings to these institutions, especially IIIT Hyderabad. These three offer research oriented academics. They even offer UG research programs. 

IIIT Hyderabad, Delhi and Allahabad are performing really well in their respective fields. They should be given much more attention.

Here is the answer to your query-

The first ‘I’ in IIIT Hyderabad stands for ‘International’. It is a private ICT Research University that was founded in 1998. The first ‘I’ in IIIT Delhi stands for ‘Indrasprastha’. It is a government institute and comes under the Delhi Government. The first ‘I’ of IIIT Allahabad stands for ‘Indian’. IIITA and IIIT Pune come under the collective of institutes that are actually the IIITs, as in, the Indian Institutes of Information Technology.

IIIT Allahabad is one of the 5 IIITs that were formed by MoE, and it has the tag ‘Institute of National Importance’. IIIT Pune is among the other 20 IIITs that were formed under the PPP (Public Private Partnership) model. It is also an Institute of National Importance.

IIIT Hyderabad is one of the best in India for CS. The CS department of IIITH boasts of top-notch placements, a good number of entrants into GSoC, and high participation rates in Competitive Programming. 

Only IIIT Allahabad and IIIT Pune belong to the collective of Indian Institutes of Information Technology. The other institutions mentioned by you are different from this group.

Colleges like NSUT and MNNIT Allahabad have a legacy built over many years. IIIT Delhi will take some time to catch up to the reputation of these colleges.

Regardless, I have tried to rank the three on several parameters, for their CS (CoE) program-

• Coding Culture- NSUT has the best coding culture, followed by MNNIT.

• Curriculum- IIITD has the best curriculum, followed by MNNIT.

• Research and Higher Studies- IIITD offers the best research prospects, followed by NSUT.

• Fests and Clubs- NSUT offers the best fests and clubs, followed by IIITD.

• Infrastructure and facilities- NSUT has the best infrastructure among the three, while MNNIT lags far behind the other two.

• Peer performance- NSUT has the best peer performance, followed by IIITD.

• Faculty-IIITD has the best faculty, while MNNIT and NSUT are at par.

• Alumni Network- MNNIT has a slightly better alumni network than NSUT, while IIITD lags far behind the other two.

Regardless of whichever college you choose for your CS (CoE), your success will come from your own efforts. By studying diligently and polishing your skills, you will land a well paying job, regardless of your graduation college.

Based on my research, I will present some points to support the opinion that I will put by the end of my answer-

• Faculty- The faculty of IIIT Delhi is considered to be one of the best in India. The college offers top-quality classroom teaching. But even IIITB has good professors. 

• Curriculum- IIITD offers the most relevant and flexible curriculum for B.Tech CSE. They will teach you core CS from the first year itself. Even IIITB teaches core CS from the first year, but it started with iM.Tech quite recently, in 2017. IIITB doesn’t offer B.Tech courses. 

• Funding and perks- As IIIT Delhi is a state government-run institute, it gets funding and other perks.

• Infrastructure and Internet facilities- Being a new institute, IIIT Delhi has better infrastructure and Internet facilities. 

IIIT Bangalore is a better choice for an M.Tech CS, based on curriculum, placements, etc. But as far as UG studies are concerned, B.Tech CS at IIIT Delhi is better than iM.Tech CS at IIIT Bangalore.

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.