I have designed and installed thousands of squares of SBS Modified bitumen by mopping the first ply and torching the cap sheet. SBS takes much less heat than APP, Maybe thats what has given you trouble. There are definitely differences in the quality of sheets however, thats why I recommended the two that I did.
Cold process has come on strong in the last few years, however, and it is probably a good choice for a homeowner with a small roof, due to the chance of fire when using a torch.
I guess we all have our preferences. My first encounter with Mod Bit was with Rhoflex, which was a hybrid Mod bit, containing both APP and SBS. The roofs I installed back in the 80's with Rhoflex in a single ply over a glass base sheet are still performing well. They had good drainage, and have been coated with fibered aluminum twice.
I think Rhoflex was sold to Firestone quite a few years ago.