Mechanical at IIT Bhubaneswar and Mechanical at IIT Jodhpur both are well-recognized in India. However, the choice between the two majorly depends on your personal preference and career goals. If you will ask me I will say IIT Bhubaneswar is a better choice as it is known for its high standards in academics and research works.
Every branch has its own unique features that might be more appropriate in line with your preference. As it is not possible to study in all the IITs, one may have only a little knowledge about other institutes - not enough to quench your thirst for information.
Talking of IIT Bhubaneswar, it has one of the best mechanical departments in all mediocre IITs, with quite an experienced faculty and really experienced professors.
Coming to IIT Jodhpur, it follows a curriculum that is comparable to most of the old IITs and being a new IIT, you may have a chance to have an opportunity regarding changes in the course curriculum. The school has got one of the best pool of Faculty Members with great work experience in analysis and teaching.
Before swinging your finger down on one Institute, you can seek advice from as many seniors as you’ll be able to and build a hip and right call.