Since the Theocracy has paladins, I'll assume they are LG. Since they are LG, they would only attack the Mageocracy if they were evil, so I'll assume the mages are evil.
In the opening bouts of the war, The mages would dominate with flying wizards with wands of Fireballs and Icestorms would cut huge swaths in the holyman lines. Entire troupes of the Wizard's warriors would march behind clerical lines under invisbility and attack with hasted swords bulgeing with Bull's Strength.
After the intial shock of getting their asses handed to them, the clerics would regroup and start useing group prayers to banish foregin magics from their camps, use stirring speeches to rally the troops, getting them into a frenzy. Paladins weilding holy swords would lead their blood lusted troops into the fray, pushing back the wizards across to the last lines of their defense. On the feild, the wizards would be routed for a time.
The clerics would close in on the Wizard towers, when they are met by a hybrid warrior they were not expecting, Fighter/Wizard multi-class. Fighters shooting magic missles and lighting bolts while cutting down men would halt the clerical advance. Wizard's useing fantastic illusionary would dupe the clerics into vulnrable postions and devistate them. Here the clerical advance is halted and brought back and a stalemate accures.
Now stalemated, by day bloody fighting would accure and both sides would dig in ( Trenches, etc, etc ) franticly but clerical healing would keep the edge and make slow gains. By night the wizards under the cover of darkness would weild terrible magic, spells of death and destruction would rain down. High Priests and Arch mages would openly ruin one another in loud destructive duels. Wizards would gain the upper hand here.
The Stalemate would be broken by a clerical charge sending the wizard's normal force scattering and retreating. The clerics again push hard, looking for a death blow and end this conflict. Wizard/Fighters would take the feild again, this time aided by numerous Golems of Iron, Stone and Clay. This would once again halt the clerical advance, but moral is high and their soliders will not budge. Here the wizards really dig deep into their bag of tricks and try everything, spreading diseases and poisioning the water source affects some men, but the clerics quickly take care of such threats. Some wizards even chance to start raiseing dead, sending droves of Zombies and Skelatons into clerical camps only to have them deystroyed without great effort.
The Fighter/Wizard hybrids finally break, too few to begin with, they have lost too much of their numbers to hold the lines anymore and the remiaing wizard troop forces and multiclass fighters flee for the towers to regroup. Now the clerics really begin to press their Arcane foes. Seige engines are brought forth and luanch a seige on the wizard towers. The Arcane masters in return, launch magical fireballs and Icestroms, doing the best they can to return fire.
Now the Arcane masters decide to end this fight for once and fore all. Their resouces are all but depleted. No longer can they mass produce wands of fireballs and such and the number of fighting men grow shorter everyday. A number of them teleport out and to the other side of the battle feild, behind enemy lines and begin useing conjureing spells, summing creatures from all over the planes and the earth. With these foul beings at hand they attack the clerical lines from behind, while the towers luanch their own assult with what golems and soliders they have left. A terrible battle ensues as soliders of purity and light struggle against vile evil creatures for their life. Priests and Paladins do their best banish foes from their plane and a mounted Calvary strike from fresh reinforcements ride in and seize the day.
Combat engulfs the first few towers as mages use retributive stikres with their precious staves to finish themselves off and take down soliders with them. Towers burn and blaze with holy fire. Mass charms are shot off, but don't turn the tide is the slighest as moral is too high for men to affected in great numbers. It seems the Arcane Masters have lost.
Or have they? Metor swarms light the sky, wishes are uttered as the last few arch-mages kill themselves and who ever else in blaze of glory, cutting large swaths in Divine lines.But the last few Archmages gather in the last tower and begin a dark ritual. They summon Orcus with all their power and offer him the plane, scaraficeing themselves in the process. Abyssal gates open and demons flood in with great numbers. Wizartds,Cleric and Paladin alike are taken down. The war belongs to the demons.
So, the Wizards win by defualt, but the real victory belongs to Orcus
