OK, a few benefits that religious civs should gain:
1) cheaper religious improvements, just as in civ3.
2) Greater resistance to conversion by outside faiths.
3) More rapid 'discovery' of new belief systems.
4) More likelihood of a new belief system or sect 'appearing' amongst a section of your community (which is both a blessing and a curse, depending on how you look at it).
5) Greater chance of religious great leaders appearing in your civ.
This would be offset by certain restrictions:
1) Your Theism level can not be below a certain level. This impacts on the influence of your religious faction, and makes relations with civs of other faiths more difficult, AND can limit your science output.
2) Greater Risk of suffering from Religious Schisms, assuming you have different sects or relgions within your nation-and that they are a big enough grouping within your nation.
Note, though, that I believe in evolving traits. Within this, it might be possible for a religious civ to shed its religious trait if it abandons religion-within its gameplay style-and favours a different trait, for a sufficient length of time.
Yours,
Aussie_Lurker.