Chaitanya Bharathi Institute of Technology, Hyderabad

IIIT Hyderabad : International Institute of Information Technology, Hyderabad (IIITH) is an autonomous university, founded as a not-for-profit public private partnership (N-PPP) in 1998, and is the first IIIT in India under this model. The important facts about the IIIT H are given below.
1. NIRF Ranking : 82
2. Accredited at Grade A by National Assessment & Accreditation Council (NAAC) in Sept 2011
3. Ranked in the top 5 overall and #1 in campus placement, among all technology schools in the country, including the IITs, by Dataquest, India's leading IT publication, in 2011. CBIT Hyderabad : CHAITANYA BHARATHI INSTITUTE OF TECHNOLOGY, established in the Year 1979, esteemed as the Premier Engineering Institute in the States of Telangana and Andhra Pradesh, was promoted by a Group of Visionaries from varied Professions of Engineering, Medical, Legal and Management, with an Objective to facilitate the Best Engineering and Management Education to the Students. The important facts about the CBIT are given below.
1. Accredited by National Assessment and Accreditation Council (NAAC) with A Grade.
2. All UG Engineering and 5 PG Programs have been Accredited by National Board of Accreditation.
3. CBIT is permanently Affiliated to Osmania University, Hyderabad.
4. Autonomous Institution (UGC Approved) since 2013.
5. NIRF ranking : 100
So I will go with IIIT-Hyderabad.

Apart from the entrance exam score and other required criteria, one major issue could be that you are not Maharashtra state candidate, read on for details about it.COEP is an autonomous college and is fully aided by Govt of Maharashtra .
For getting admissions into fully aided autonomous engineering colleges of Maharashtra one of the eligibility criteria is: You should have one of the Maharashtra State Type Candidature( A to E ) as defined by DTE, Maharashtra.
Type A: Students passing SSC and HSC (or diploma) from Maharashtra and is either born in Maharashtra or is the domicile of Maharashtra.
Type B: a student who is not of Type A but whose father or mother is domiciled in Maharashtra.
Type C: a student who is not of Type A or B and whose one of the parent is employee of Govt of India and is currently posted in Maharashtra.
Type D: student who is not of Type A or B or C and whose one of the parent is employee of Govt of Maharashtra (current or retired)
Type E: a student who is not of Type A to D and who passed SSC and HSC from one of the institutions located in Maharashtra Karnataka disputed border and whose mother tongue is Marathi.