The difference between beats solo by dre and beats studio by dre is the size and sound quality. The first tend to be so small like the fist size while the second are of average size. The sound quality in the first is also lower as compared to that of the beats studio.
Beats by Dr. Dre Solos are "on ear" and are noise reducing. They do cancel out some of the noise because they fit so flush on your ear. The Beat's Solos are 200 and they say that the headphones snap easily; they also only come with one cord.
Beats by Dr. Dre Studios are "over ear" and are noise canceling with two AAA batteries. They will cancel out most, if not all of the outside noise. Beat's Studios are 300 and are a little more durable. They come with two separate cords. One purely for music and one for music and talking on your iPhone.