Erm no? Not better, just different.It works better for someone like the OP who obviously wants to play a melee/caster hybrid.
An inquisitor needs to cast 1 standard action buff and use 2 swift action class abilities to do really good damage with a weapon.
A cleric needs 2 standard action buffs, one of which only kicks in at level 9 ... and even then his damage output just won't be that good, especially with a shield. From 6-8 and/or if he doesn't have time to prepare for a fight he will look very very substandard compared to a real martial character if he tries to use a weapon instead of cast spells.
On top of that, a good portion of a battle cleric's daily mojo at high level is spent on buffs that bring him up to par with a typical melee character. That isn't so bad, as lots of classes have heavy prep to do at high level. However, it really doesn't support the theory that a Battle Cleric is a "full casting" class and a melee fighter. They have to choose either or every time they sit down to pray for spells.
That argument aside, you then have a heavily buff dependant character that flat out requires those buffs to compete (never mind that the other melee characters are sporting many of the same buffs which make them even cooler). All you need to take that apart is Dispel Magic or any other antimagic/magic supression effect that becomes more and more readily available from foes and encounter design at high level. I can tell you from personal experience that even one event like that can ruin a play session for the "player," and at the end of the day when all the numbers are set aside that is what is really the most important...having fun.
The concept is cool as heck, and it is possible for a battle Cleric to be made effictively on a cleric chasis (the crunching numbers, buff applications and such mentioned so far are solid...the battle cleric CAN work). I'd just still recommend building that character concept as an Inquisitor to make sure it is both cool and fun. Besides, it's not like the player has to run around saying "Hi my name is Edgar the Inquisitor." He could still, for roleplaying purposes, be a member of the clergy of any church he wanted.
He just gets to roll two extra damage dice as he decides to have a human bane earthbreaker this round, and assume the most appropriate team work feat for the occaision...and he can cast a spell next round...all the while judging the crap out of his god's enemies.