Double jointed oval mouths (also called a lozenge) tend to be the gentlest type of mouthpiece. They are milder than french links (normally) because of the rounder mouth piece.
If your horse has a big mouth, high palate, especially with a small tongue, thick mouthpieces will be milder because of the bigger surface area where the bit touches the horses mouth. If your horse has a low palate and/or big tongue, a thicker mouthpiece will be more severe as it wont fit the horses mouth as well, a slight movement of the rein and it moves into the horses tongue or bars.
“Good things come to those who wait… greater things come to those who get off their *** and do anything to make it happen.” - Unknown