IIT Dhanbad is one of the oldest IITs, so it is a good choice to study MTech in EEE from there. However, being a student of IIT Bhubaneswar I would suggest opting for MTech in EEE from IIT Bhubaneswar.
B.Tech courses are preferred than MTech. courses by most students as BTech courses offer more placements. M.Tech is a more research-based program.
IIT Dhanbad is an older institution than IIT Bhubaneswar and offers a large alumni base. IIT Dhanbad ranks 42 among Indian universities.
If you are interested in taking up a research-based course that focuses more on academics you can opt for MTech in EEE from IIT Bhubaneswar but if you are looking for placements then a BTech in EEE from IIT Dhanbad will be better.
As IIT Dhanbad is a more reputed Institute when it comes to reliability. 75% students are placed in IIT Dhanbad in this year in the EEE department (BTech). The average salary offered to an EEE graduate is 15.5 lakhs per annum. MTech Students from IIT Bhubaneswar have a 68% placement rate in Core Engineering Departments, being offered a salary package of 10-16 lakhs per annum.
Lastly, it depends on your choice but to study MTech in EEE you need to complete BTech with at least 60% in aggregate. If you want to research further instead of working MTech will be a better choice after your graduation.