As Mike Sullivan states, the Mystic Theurge is an attempt to make spell-casting multiclassing as useful and tempting as a level of rogue or fighter.
I think this prc accomplishes its goal well, and as far as balanced it comes up fair. First, you have to preclude allowing the character to take a level of True Necromancer (a first level ability which stacks cleric and wizard levels for the casting level of necromancies would be quite broken), and then you have to consider other clr/wiz prcs to see if there is another uber broken quality when in conjunction with the theurge.
If youve determined that that issue is ok, the theurge isnt really overpowered, just different. He has quite a bit of endurance, as in able to cast spells more often than a sorceror, but with considerably less power.
I believe any comparison to Theurge and Cleric comes with cleric on top, as the cleric retains her better BAB, better saves, better HP, turning ability, and the ability to cast divine spells in armor, all of which the theurge loses. The big comparison is with a straight wizard and the theurge.
3/3/1 Theurge vs 7 Wizard
The wizard's spells are so much better the comparison is almost moot. The wizard also has a leg up on familiar advancement, and 1 more feat. The wizard will probably be looking to enter a prc himself soon, but we will assume he stays straight wizard.
Theurge Spells Per Day: Clr 5/4/3. Wiz 4/3/2
Wizard Spells Per Day: 4/4/3/2/1
There are 2 big comparisons, highest spell level and total spells. For the purpose of this argument, 0 level spells are not considered. The Theurge has 12 spells and his highest is level 2. The Wizard has 10 and her highest level is 4. Clearly, this is no contest, the Theurge has only begun to become a viable character concept.
3/3/4 Theurge vs 10 Wizard
The wizard has gained another feat and at this point can communicate with his familiar telepathically. The theurge has achieved a 7th level caster in both arcane and divine magic.
Theurge Spells Per Day: Clr 6/5/4/3/2. Wiz 4/4/3/2/1
Wizard Spells Per Day: 4/4/4/3/3/2
The Theurge has 22 spells and highest level 4. The wizard has 16 spells, highest level 5. The theurge is approaching the power of the wizard, but will never beat it. A theurge can cast a fireball for 7d6 damage, with a spell penetration of +7. The wizard casts a fireball for 10d6 damage, with a spell penetration of +10, or could use a 5th level slot for an empowered fireball.
Its important to point out that as far as buffing fellow party members, the theurge is unparalleled. His ability to summon monsters is also strong, as the odds of running out of spells is smaller.
3/3/7 Theurge vs 13 Wizard
The wizard's familiar has gained spell resistance and the ability to be scried by its master, but the wizard is still only 2 bonus feats up on the theurge.
Theurge Spells Per Day: Clr 6/5/5/4/4/3. Wiz 4/4/4/3/3/2
Wizard Spells Per Day: 4/4/4/4/3/2/1
The theurge is really pulling his own weight, with a whopping 37 spells per day, highest level 5th. However the wizard has advanced far enough to get 7th level spells, and despite his smaller amount of spells per day (a mere 18, less than half of the theurge) they are more potent. Compare the Theurge's Cone of Cold at 10d6 and 50 ft to the Wizard's at 13d6 and 65 ft. Comprable? Yes, but the wizard could cast a still and silent version as a level 7 spell, or a Prismatic Spray. The Wizard also retains a +3 relative to the Theurge on Spell Penetration rolls.
At this point its prudent to consider costs. The theurge will probably be saving on some scribing costs, as overlapping divine and arcane spells dont need to be scribed, but the theurge has 2 important mental statistics. Also, despite his strong role as a buff-stick for the party, his buffs lasts 3 caster levels less than the wizard, and are 3 caster levels easier to dispel.
3/3/10 Theurge vs 16 Wizard
A close showdown, this is the theurge at the height of his power as after this level he will have to take single class levels or another prc.
Theurge Spells Per Day: Clr 6/6/6/5/5/4/3/2. Wiz 4/4/4/4/3/2/1.
Wizard Spells Per Day: 4/4/4/4/4/4/3/3/2
The Theurge is up to 50 spells a day, highest level 7. The Wizard has picked up a third bonus wizard feat and has almost reached 9th level spells. With 28 spells and up to level 8 spells, the Theurge has managed to pull ahead. His spells arent quite as potent, and are still behind the Wizards' in terms of penetration, but if he can live long enough to cast them he has more force.
Its also noteworthy to point out that if a Theurge took Cleric as his starting class, he will have perhaps 10 more hp and by level 16 equal saving throws except Will, which is 3 higher for the Theurge. While he has been able to advance most of his skills as a straight wizard, he has lost Scry as a class skill, a potentially powerful loss for a high level spellcaster. If he chose to have a familiar at all, it is little more than a hindrance, as its death will only harm the character, and it is not nearly as hardy as the Wizard's counterpart.
This discussion did not take bonus spells into account, but the theurge would probably benefit almost twice as much as the Wizard. 3e encounters are difficult to balance at high levels, when a single high level spell the monster doesnt manage to save against spells the end of the encounter. For the Theurge, the odds of a 1-spell answer working are far lower, especially against "boss" encounters (CR 1-3 levels higher than party).
I maintain that this prc is really only powerful if you begin play at higher than 9th level, as up till that point the Theurge (or multiclassed wiz/clr) is significantly less powerful than a single class combination (or a spell-fighter combination). It is not until the highest level of play that a theurge comes into his own, and at that point he has more spells than he can use in a day. It is also in the Theurge's greatest benefit to acquire this class as quickly as possible (right after getting clr3/wiz3), slower acquisition means longer that you are "underpowered".
Technik