Something like this :
Focused Transmuter Edition (either HalEld or Red Wiz):Pros-
-Access to all spells through one school (so Red Wizard prefered to cash in on the bonuses from that)
-0 lost casting progression
-Spontaneous access through Spell Engine abuse, and/or at will miracle
-Mythal capable
Cons-
-Less spontaneous capabilities (i.e. none native outside of DCFS)
-No epic spell capability unless built into the mythal
-Requires Savage Species for at will miracle
-Relies upon cheese with a ToAL
-Same limits on spells/round as any other caster (1 standard, 1 quickened, possibly one additional as an immediate, borrowing against next round)
Focused Illusionist Shadowcraft Mage edition:Pros-
-Casting high level spells from low level slots
-Spontaneous casting without needing an item or Profession (Diplomat)
-Sidesteps Casting Time and Material Components on spells like Major Creation and Genesis
-Easy Access to Epic spells such as mythals
-More automatically applied metamagic (as everything starts out as a Silent Image)
Cons-
-Feat Tight until DCFS antics come in
-Same limits on spells/round as any other caster (1 standard, 1 quickened, possibly one additional as an immediate, borrowing against next round)
-Universally relies upon SR, though this is somewhat mitigated by having ungodly CL (which all three have)
Elven War Weaver Incantaluuran:Pros-
-Mass self and party buff via 7-8 spells cast into the tapestry and left latent until needed (can even be left in overnight)
-Not shackled to the same action routine, as they add in those 7-8 spells as a move action, and still can move via Ride on a Phantom Steed
-CL 40 means the natural buffing nature of the War Weaver is augmented even more by being nigh impossible to dispel
-"Offensive tapestry" via Reach Spell (also used to get usually unusable spells into the normal tapestry) and Chain Spell, and the feats/abilities to mitigate their cost to nil.
-Ability to sell out all else to action economy and initiative (elven substitution with a hummingbird)
Cons-
-Two lost levels of progression
-A lot more bookwork needed, as cranking those slots meant for buffing up to 20th level slots means no tapestry for them
-Relies upon creation of a Legacy Item
In SummaryIn terms of raw breakthrough power, the Red Wizard Transmuter has the highest CL of the three, and the highest spell penetration. His nukes will be that much more nuclear, and he's tied with the SCM for raw number of slots available to heighten to 20th level. He won't have quite the metamagic reduction the other two will have though, as they both use Halruuan Elder.
The Shadowcraft Mage is undeniably the most versatile, having multiple ways of getting shadow miracles and play godbuilder in ways a Cheater only dreams of. They've also got the easiest path to epic spells pre-epic, this side of koboldy-pun. Oh, and they can burn their spellbook, and not miss a single page.
Finally, the Elven Weaver will be both his own and his party's best friend, as he can uberbuff the lot of them with just one move action, and from all the different factors contributing, he's going first. Even rolling a 1, with pretty standard gear he'd be getting at least a 25, assuming a 20 dex after buffs, and with standard initiative boosting gear. Add 4 more if Belt of Battle and Sandals of the Vagabond are included. And that's on a 1
He has fewer raw spell slots, but the same CL as the SCM and the same capability in boosting his slots to 20th level, though some of them won't be going that high (thus saving time) to facilitate stocking the tapestry. Between all the passives from his Legacy Toy, his head start on the action arms race, and his extra missle in the Tapestry, IMHO he's got it. While not as easily Epic Spell endowed as the SCM, and lacking a few CL on the Red Wizard, he's got the one advantage that trumps all of them, and that's more he can do at once.