To my understanding the mullen is more of a 'straight
bar' mouthpiece (depending on whose terminology
you use) which can be very harsh putting pressure
on the tongue - especially if a horse has a 'thick
tongue'. The 'arch port' or 'sweetwater' allows
for total tongue relief and applies pressure directly to the
bars and corners of the mouth but is short enough
to not strike the palate. It is considered the milder
mouthpiece. The port must be 2" or more before
palate pressure is obtained. All snaffles are fairly mild -
'single joint', 'french snaffle (double joint)',
'dog bone', some have rollers and players to keep the mouth
occupied and stimulate saliva. The twisted wire
snaffles are harder on the bars. Generally the thicker the
mouthpiece the milder it is and the thinner the
mouthpiece the more severe it is.