I feel it is an error to underestimate the potential threat that was presented by this Galilean cult. As I understand it, they did have a powerful weapon in their armoury, in that their proselytising was largely driven by notions of equality and mercy; indeed, it is said that their founder/leader had claimed that the meek would inherit the Earth! As outlandish as this sounds to modern ears, we should not discount the appeal of such saccharine sedition to the plebs, surely leading to social instability. And if such notions had caught hold in the Legions, discipline would have been sorely tested, and fighting spirit badly sapped by such doctrines as "Blessed are the peacemakers". Indeed, it was only due to the sterling vigilance of men such as Saul of Tarsus (sadly killed in the line of duty on the road to Damascus) that this subversive cult was supressed in time to stop any deleterious effects upon the Empire; without his tireless efforts, the world may have been a very different place today.
Unfortunately like many people you overlook the fact that 'this Galillean cult' still exists today, and in fact I am a member. Now it is a shame we are not so well known in the modern world, partly due to the fact that most of us went underground as a rsult of the intense persecution we suffered in those days. Even in our own 'enlightened' times it seems like few people actually understand what we are actually about, as your attitude clearly demonstrate. This is hardly surprising, since the attitude of Yeshua (also called by the Greek form of His name, Iesous or Jesus) was quite the opposite of the world at large. The Christian (as we call ourselves- possibly a derivation of the Greek word for messiah or anointed one, Yeshua's title) view of power, for one, is shown in servitude and weakness, not by the traditional Roman ideal of might. This is part of the significance of Jesus' crucifixion, as I will explain in another post.
Now I doubt that Christianity could ever have had the same impact as Mithraism did on the Empire, since Christian teaching clearly states we are supposed to be separate from the world (not quite as extremely as some sects sadly teach, or else I would not be posting on this forum!) and n order to do that, somehow it would have had to gain favour with the Emperor and be established in a similar way. This would have involved corruption of the very teachings which we hold dear- but then, it isn't exactly like Mithraism wasn't either, as some Mithraic fundamentalists claim the revelation of Sextus Longinus was?
As for Saul of Tarsus, Christian tradition maintains that he wasn't actually killed, but actually was converted on the road to Damascus when Yeshua appeared to him in a vision. What we know of him is mainly known by he early Christian writer, Loukas of Antioch who was said to have been associated with him. It is normally suggested that the account of his death was later fabricated by the Jews in order to cover their own shame. According to Loukas, he actually became an influential figure in early Chritianity and actually spread it throughout the Empire. Some of his writings are thought to survive but this cannot be verified.
[RL note- I've tried to write this in the spirit of the DBWI, as a Christian viewpoint of how it could have become less sucessful. I've taken a few liberties with Saul/Paul- his writings being largely unknown- but for him to be written out to be virtually written out of history, they would have to be (almost!) lost! How Christianity might have turned out in such an event I leave to you! BTW, Loukas is the Greek form of Luke, who was thought to have come from Antioch.]