The main difference between the two machines is the size.
The Major has a 6.7L bowl and the Chef a 4.6L bowl.
The motor size will also be higher for a Major verses its comparable Chef sized machine. For example, the KM631 Major Classic has 900w power compared with the KM336 Chef Classic which has 800w power.
It is worth noting that the Major is a taller and heavier machine as it can mix larger quantities at one time.