Pros:
2 Domains and an inquisition
Channel energy
Judgments
Stern Gaze/monster Lore
Cons:
Weaken spellcasting [you will have a lot of 1st level spells, but as you progress, your spells are lower level as opposed to a single class(lvl 10 cleric has lvl 5 spells while a 5 cleric 5 inquisitor has C: lvl 3, I: lvl 2)]
Weaken judgments(vs a single class) [effect is not visible till later levels]
Weaken Channel(vs a single class) [DC is lower, less dice as you advance, not visible till later levels]
Weaken Inquisitor abilities that depend on level (stern gaze, track)
Slower to gain many of the inquisitor abilities
In the begining, you come out slightly ahead of a cleric due to the extra skill points and abilities an inquisitor gives but the benefit quickly drops away. For example, your BaB is +0 as a Cleric 1, Inquisitor 1. If you went Cleric or Inquisitor 2 you would have a +1.
I would recommend straight inquisitor, it is a lot of fun and should give the party whatever it needs (it can still spontaneously cast cure spells along with any spell it knows)