I think that, if there to be ONE SET of key differences between religion types, it would be the chance of religious conversion and the chance of a religious schism.
Basically, your non-deist faiths (i.e. ones based around philosophical principles) would be the MOST susceptible to religious conversions, as adopting another religion would not be seen as offensive to their current belief structure. By the same token, though, they are the MOST resistant to religious schisms, as they are less dogmatic and more accepting of difference and change.
Your Polytheistic and Animistic faiths are a little less prone to conversions, but are still fairly susceptible to it due to the wide range of choices they already have within their pantheon! Many Polytheistic cultures had various sects and cults rising and falling on a regular basis. In Rome, for example, the Mithraic Cult thrived as one of the first genuine monotheistic faiths in that region, but soon died out. Later, the 'Jesus Sect' of the Hebrew faith converted many Romans to its beliefs, before finally becoming the official religion of the Roman Empire-by which time they had changed their name to Christianity. For these reasons, polytheistic religions are also slightly more susceptible to religious schisms than non-deists.
Lastly, Monotheistic faiths are the LEAST susceptible to conversion, as the authorities tend to push a VERY hard line regarding that faith being the ONE TRUE FAITH! Due to their heavy reliance on Dogma, these faiths are also the MOST susceptible to religious schisms. The Jewish, Christian and Muslim faiths have all broken into sectarianism (look at the Essenes vs the Hassidics; the Protestants vs the Catholics and the Evangelicals, and the Sunni vs the Shi'ite and Wahaabi-just to name a few historical examples!)
Obviously, what I have put up relates to situations where 'all other things are equal'! Other factors, such as corruption, unhappiness, relative culture levels and distance from the Religious Capital (if any), as well as your peoples degree of 'spiritualism' will all effect the actual chances.
Yours,
Aussie_Lurker.