Does it do with every modeled guitars (tele, strats, les paul) on that particular patches or only lets say les pauls? These patches might have been made for guitar with "low gain" pickups and to compensate this, authors could put let's say some compresors (or eq with higher gain) to compensate this. Does it also do when you lower modeled guitar volume using volume pod on Variax?

If you are using your JTV with the HD500, it could be something as simple as accidentally saving the patch with the tone turned down.  I've done that several times during rehearsals and didn't figure out the problem until I got back home to work it out.  So when you turn off the modelling and go with the mag pickups it sounds good.  If then after switching the modelling back on it sounds muffled and bassy -- adjust the tone knob on your JTV -- problem solved.