For most audiophiles, choosing an open-back headphone over closed-back is a no brainer as long as you have a quiet environment and aren’t going to disturb anyone nearby, as the music will leak out of the headphones. Open-back headphones allow air to flow freely through the ear cups, resulting in more a natural, transparent sounding headphone.
The best dynamic, planar-magnetic, and electrostatic headphones are all open-back designs. Many regard the STAX SR-009S or HIFIMAN Shangri-la Sr. as contenders for world’s best headphone. For down-to-Earth budgets consider the HIFIMAN Sundara or Sennheiser HD660S.