Based on national averages and midrange remodels, finishing an attic space into a bedroom with a bath (shower only) will cost about 26% less than finishing a basement the same way.

So does it cost more to finish an attic or a basement?  The answer is it costs less!  This comparison can change significantly if factors and features of the remodel are very different. If, for example, a major remodel of the existing structure below the attic is necessary to build a stairway, the cost difference will be less. On the other hand, if the basement is not wired for electricity or equipped with plumbing and will require a sewer pump and extensive systems to accommodate a bathroom addition its cost will increase.

Quick link:  Finish a basement cost estimates

The best way to answer this question is to make as many decisions about the living space you want to create and gather as much information as possible about the two areas (basement and attic) and factors that could affect the remodeling cost. Then use either an online remodeling estimate calculator or contact a local contractor to find out what the difference in cost will be for the project you are considering and for your specific location.