ECE and EEE, most of the syllabus is same and the subjects are considered as electrical core subjects like analog, digital electronics, signals, networks, etc. With courses being almost the same, the comparison comes down to other aspects of institutes.
If you aim to get good placement packages after finishing your degree to work then you should opt EE in IIT Bhubaneswar. In 2019 placement 86% EE batch was employed. PSUs hire directly from IITs with the new mandate by the government which gives students in IIT to pursue a career in PSU without having to clear GATE. Although for ECE the placement of IIIT Hyderabad is higher (10 LPA) compared to IIT Bhubaneswar.
IIIT Hyderabad also provides great infrastructure and laboratories and have been very well funded for research papers. IITs get their funds from the Govt. and both institutes are on equal pace in this aspect.
Campus life can be one more aspect that students may find interesting while selecting the course and college. Academics in IIIT Hyderabad ECE is considered to be advantageous compared to IIT Bhubaneswar EE, because of IIT BBS is a new institute.
Faculty members at IIIT Hyderabad are also some of the highly eligible professors and some of them are from old IITs.
Overall, when comparing both courses and institutes, IIIT Hyderabad comes on top, but the choice should be branch instead of college when both have equal pros and cons.