I have biked all of the Badlands and much of the Black Hills over the years.
There is a BIG, BIG difference between the two - especially in summer.
The Badlands has almost no shade and can be brutally hot.
The Black Hills are ideal in summer - lots of mixed forests and meadows, camping.
I wouldn't restrict myself to the Mickelson Trail -
many of the unpaved forest roads offer great riding for anyone with experience.