Civil Engineering

Civil is more of a core branch while design is not. It completely depends on your interests as to decide where you should go. Institutes do matter but branch matters a lot more.
Quality of teaching: I can tell you that civil department professors at IIT-Bhubaneswar are quite good. Although I don't know much about the professors at IIT-Guwahati but still, IIT-Guwahati being older will be equally good if not better.
Campus life: IIT-Guwahati has a much better campus life than IIT-Bhubaneswar, so there will be much better exposure. But newer IITs are improving at a fast rate. There will be fewer students in IIT-Bhubaneswar compared to IIT-Guwahati so there are better opportunities for an individual to actively participate in extra academics activities like societies and fests. Although sports facilities at IIT Guwahati are much better than IIT-Bhubaneswar.
Placements: IIT-Guwahati design will be mostly offering non-core placements while at IIT-Bhubaneswar you have a much better chance to get core placements (this year more than 70 percent students got core placements). So, if you have more interest in the technical stuff then I would suggest IIT-Bhubaneswar civil as a better choice over IIT-Guwahati design. The average package for IIT-Guwahati design will be greater than IIT-Bhubaneswar's civil branch.