There are a number of deities that have low-damaging weapons as their favored weapon, like daggers and gauntlets. Sharess for example has the Claw Bracer as her favored weapon, which according to the Arms and Equipment guide deals a meager 1d4 damage.
Compared to other weapons like the heavy mace, the longspear and the morningstar and their 1d8 damage this is a pittance. Additionally, these are simple weapons and do not require an Exotic Weapon feat to be able to use them, like a Claw Bracer is.
Are there any mechanical reasons for the Cleric to use a less-damaging but deity-favored weapon over a weapon that deals more damage?
I am aware that the PHB (strangely not the SRD though) mentions that it is a "point of pride", but this is not a hard limitation.