You can control the "shape" of the preamp and power amp distortion. The Preamp Hardness parameter controls the shape of the triode emulations. The lower the value the softer the distortion. The Power Amp Hardness controls the power amp clipping but that often is not noticeable because negative feedback around the power amp makes the distortion harder. Therefore you can make the power amp distortion softer by reducing Negative Feedback. A good example of this is a JCM800. A JCM800 has very hard preamp distortion (since there is no cathode bypass cap on the last stage) but has low negative feedback which softens the power amp distortion. The trick with that amp is to get the amp into the sweet spot by increasing the MV until you are getting some power amp distortion which softens the preamp distortion.
Another factor which controls power amp hardness is Transformer Match. There are two primary distortion mechanisms in a power amp: grid clipping and plate clipping (PI clipping notwithstanding as this is only audible with a post-PI MV). Grid Clipping is extremely hard, almost a hard clipper (i.e. if(x>a) then x=a). Plate clipping is much softer. However most power amps are slightly undermatched which means the grids clip before the plates clip, but only at those frequencies where the speaker impedance is "nominal". At high frequencies (above 1kHz or so) the rising impedance of the speaker causes the plates to clip before the grids. At the low frequency resonance the plates also clip first.
If you increase the transformer matching the plates will clip earlier and, since plate clipping is softer, the distortion will be softer. So turn up the Transformer Match and turn down Negative Feedback for softer power amp distortion.
However... designers know all this and they design an amp to sound best in a mix (at least the good ones do). Soft clipping sounds great when you are playing by yourself but as soon as you are in a band context the sound gets lost since hard clipping helps cut through the mix. Amps designed for rock typically have harder clipping than an amp designed for blues or jazz. A 5150, for example, has an extreme amount of negative feedback which makes the power amp very linear and clips very hard. A Deluxe Reverb, otoh, has low negative feedback and large cathode bypass caps on the last preamp stage. This makes the clipping softer and the sound less "clear".
