Mages love to compare themselves to each other, especially when similar. We all know WHM cures and BLM nukes, but then we have SCH and RDM that do both, which naturally causes the other 'Polar' jobs to draw comparisons. There's nothing wrong with that, but please understand the limitations that come along with being a mixed caster.

So you can see where some of my lines of thought come from, I see SCH in the cycle of mages as BLM aligned in the spectrum.
Spectrum of Light to Dark Magic:
WHM > RDM > SCH > BLM

Keep in mind: RDM has Tier IV nukes and built in MAB. SCH has Tier V nukes and NO built in MAB. BLM has both.

SCH is not a straight caster job. Yes, all of its coolness is from having fun with what equated to D&D 3.5 Metamagic feats with spells, but that is actually what makes it not a straight caster. The main power of the job comes from the Stratagems, which are job abilities. This makes us more susceptible to Amnesia than any other Mage... and we have no Resist Amnesia traits. This is probably on purpose as a limiting factor to SCH that other straight casters don't have.

Because those Stratagems are what you base most power arguments around (for good reason), when you further layer up gear and effects like weather, you start down a slippery slope where you can start to confuse what makes SCH good inherently, and what SCH has to do to approach competitive levels with a Polar Mage.

Consider: Layering is a core concept of SCH, from layering gear, to weather effects and most prominently, layering stratagems. Some of that layering is SCH specific, but a good amount can be done on the party, too. Please try to restrain your imagination and discount what a SCH can do with full layering if at any point in the layering it can be done to you, too.

Out of the Mages, SCH is also more limited on gear choices. This also seems to be on purpose, as even our AF3+2 Body only provides 1MP Refresh. A fully geared and prepped SCH is able to reach that level of competitiveness with Polar Casters... but at what cost to the SCH in terms of inventory slots, gil/time, and having to macro all that swapping in? Are you really upset because SCH is OP? Perhaps you're seeing some fluid and extensive macroing that had to come together to get those gear swaps and job abilities firing correctly. Or are you looking at his gear over swaps and seeing some fine gear that would take forever to attain? There's nothing wrong with that, just recognize all the effort that went into that SCH spell, BEFORE it was ever cast.

Before Abyssa, in the land of level 75, SCH had mana efficiency and time on it's side. Less so in Abyssea. The main parallel to BLM drawn up on the Kanican journal was to show how, through MP Efficiency, SCH was more 'powerful' than BLM over time.
This was a warning to SE and it looks like they took parts of it seriously. In the updates they have given BLM some very fine tools 76-95 which help widen this gap (Elemental Celerity, Enmity Douse, Mana Well), and very little to SCH (One More Stratagem). This is good, as SE needs to be conservative with edits to SCH. Time, however, relates back to stratagems. We top out currently at 5 recharging ONE stratagem in 48 seconds (6 and 40 seconds if they add one through 99, which I doubt they will do or need to do). So once a SCH is out of stratagems, those awesome spells can only be cast in 48 second intervals. This means that in addition to having MP as a limiting factor in general, job abilities become a secondary limiting factor which other Mage jobs don't have in the course of casting a majority of their spells.

Hopefully with these things in mind, and with what other SCH might point out too, you can see where the trade-off in power between the jobs really happens and make more pointed and precise criticisms of SCH versus your other jobs... now RDM on the other hand...