Ideally - A design/build firm will be cheaper. The idea behind a design build firm is that they lower the overhead - increase designer to builder communication - and create synergy for customers. These can create cost savings for the customer. That is not to say they always do. Just that they should.

Theoretically they should also be more limited. A design/build firm is less likely to do things out of their comfort zone and more likely to consume savings when they do. But again, that may not be relevant to your project.

There are advantages to both project delivery methods and if done well they should have similar results for a similar price but there are a lot of variables.

To me the decision depends on how much control you want to have in all phases of the project but especially during construction, and how much you are concerned with custom detailing. Even if the design-builder is fair and competent, he will always have a conflict of interest since he can't represent both sides of the contract at the same time. Of course, it would not be as critical for an attic renovation as for an entire house.