I really think historians and people in general tend to exaggerate about Maxentius' attitude towards Christianity. Yes he was a pagan, but his persecutions against the Christians was not really very high, Gibbons states that he was "just, humane and even partial towards the afflicted Christians".
I don't really think he cared what the state religion was, he was too intent on trying to keep in power and feared an uprising from the Roman masses in Rome more than anything else.
Apparently the reason he left the safety of the walls of Rome when Constanine was approaching was that he feared that the people would riot and open the gates for Constantines army. The people had been suffering food shortages for quite a while and most of the food probably when to the army.
Maxentius' army was far larger than that of Constantine but not as well trained or experienced. Many people think that Maxentius and his forces were slain by Constantines troops but he died simply because the bridge he was on (with a large number of his troops) simply collapsed from too much weight, causing him and many armoured troops to drown.
Personally, I like Maxentius, he's one of my favourite 'Emperors', and I don't think if he won the battle it would make a difference in the long run. Christianity alrady had popular support and would eventually become a state religion. The pagan Emperors were like conservatives, trying to all costs to prevent change but the tide was slowly turning against them and all they could do was delay the outcome.
By the way, does anyone where the 'Catherine wheel' comes from? I don't know if the story behind it is true or not, but it certainly would make Maxentius seem quite the villain if a movie was made about this era.