You can't compare only max damage of both options to identify which is more effective. Such a method ignores the likelihood of that outcome occurring. If we're just going to assume best result, then Mage wins via Finger of Death (or similar instant-kill spell) every single time regardless of enemy HP. The more commonly accepted method is to look at average damage, including factoring in chances of a miss.

IGMS has a single 'attack roll' IF the enemy has spell resistance, otherwise you just deal damage. Your greataxe always has 5 separate attack rolls to make, the power attack damage is lowering the chance of the attack doing any damage at all, and the odds of getting a crit on all 5 attacks are ridiculously low (approximately 1/3,200,000, without counting the extra die rolls to confirm each is a crit).

However, lets run some very simplified math with wild assumptions all over the place, just to see how things work out.

First, assume Klauth is an Ancient Red Dragon using the stats listed here. I'll be basing most of my other research numbers from this wiki as well, just for consistency.

Level 13 Fighter has +13 (BAB), +10 (30 str), +1 (weapon focus), +3 (magic weapon) = +27 to hit. Ancient Red Dragon has AC of 39, 39-27 = 12 (minimum d20 roll needed to hit). The fighter hits with maybe 50% of his primary attacks, his first extra attack (39-22=17) hits maybe 25% of the time, and his third attack hits on nat 20. Even if he hits for max damage, his non-crit damage is 12 (greataxe) + 15 (2h str bonus) + 3 (magic weapon) + 4 (weapon spec) = 34 damage per hit. A 4x crit (greataxe + improv crit) deals up to 132 damage (again, assuming max damage). Knock 25% off his hit chance to add 5 points of Power Attack damage, or knock 50% off his hit chance to add 10 points of power attack damage.

Let's look at a Level 13 wizard:
13 (wiz lvl) + 5 (5th lvl spell) + 4 (Greater spell penetration) = +22 to break Spell Resistance for most spells that matter against stronger opponents.

Ancient Red Dragon has Spell Resistance 28, 28-22=6 so expect slightly more than 25% wizard spells that check SR will fail.

Cast Cone of Cold
Save DC: 10 + 5 (5th lvl spell) + 5 (30 int) + 2 (spell focus) = 20.
[Edit: That should be 20 int for the +5, not 30 int (which would yield +10).]
ARD reflex save is 19, so about he'll take half damage about half the time. Let's assume he makes the save every single time, since it should roughly offset his weakness to cold damage.
Spell damage is 13d6, so 3x13=39 damage (which is slightly below average).

In one round:
1 spell from Wizard, using average damage = 36 damage.
4 hits with max damage attacks from (hasted) Fighter = 34x4 = 135 damage.

Now lets account for misses.
Damage x Chance of success = expected damage

Wizard
36 x .75 = 27 damage

Fighter
34 x .5 = 17
34 x .5 = 17
34 x .25 = 8.5
132 x .05 (assume crit from 20) = 6.6
17 + 17 + 8.5 + 6.6 = 49.1

49.1 vs 27, so the Fighter wins! (as long as we compare Fighter's max damage versus Wizard's average damage, including Fighter feats to hit and damage, but not checking Wizard options from Metamagic feats (like Empower Spell).

Quick check on Wizard's damage from IGMS:
===
32d6, using 3's for slightly below average damage, yields 96 damage.
96 x .75 (beat SR) = 72.

IGMS average damage handily beats Fighter max damage.
===
Edit: I need to correct the above section. Not sure where I got that 32.
26d6 (lvl 13 x 2d6 per lvl), using 3's yields 78 damage.
78 x .75 = 58.5

IGMS average damage still handily beats Fighter max damage.
===

If we compare 15th level characters, then Wizard can now Empower IGMS, while Figher gets maybe +2 to hit.
If we compare 17th level characters, then Wizard can starting casting Time Stop and things just get silly, while the Fighter gets maybe an additional +2 to hit.