Both are more complex designs than Newtonians or Refractors. These designs are popular because of their compactness. A lens-like corrector plate bends light onto the primary mirror. After light reflects from the mirror, it travels once again up the scope to the secondary mirror integrated with the corrector plate. The returning reflection is directed to the star diagonal mirror and on to the eyepiece.
Compact tubes are easy to carry and pack.
Stubby tubes mount easily onto equatorial platforms for astro-photography or for computerized GOTO capability. Good planetary performance because of the typically high focal ratio. Many accessories available because of the popularity of Meade and Celestron brands. Very long cool-down time because of the enclosed optical design. Somewhat expensive because of the complexity, but less expensive than an equivalent refractor.