brains and brawn
Mental acuity or intelligence and great power or physical strength, considered together. Our star football player got into an Ivy League school because he has brains and brawn.
brains versus brawn
Mental acuity or intelligence in contrast to great power or physical strength. This isn't a case of brains versus brawn—you need both intelligence and physical strength in a situation like this.
brains and/versus brawn
intelligence and/compared with physical strength: In this job you need both brains and brawn.