My guess is that Attack Power is secretly boosted through levels... like a hidden attack power bonus of....
Attack Power Bonus = Attack Power + (Attack Power*(level/3)/100)
I've collected all the Phase equipment, so here's a breakdown.
Phase Cutter - +20 STR
Phase Shield - Holy resistance (didn't check for Darkness resistance, will try soon), craploads of evasion+magic evasion
Phase Helm - +20 SPR, INT, Ice resistance
Phase Body - +20 STA, Fire resistance
Phase Knuckles - +20 AGI, Lightning resistance
The Phase Body is overrated, since the other armors can provide more useful bonuses... but it does increase evasion which I guess is nice.

Also, I found out you can cast Arise on a character, despite them not being dead. Apparently it heals the target to the max anyways.

Phase Shield has no Darkness resistance (not that it matters).
Also, Machine Break breaks down to the combination of Cid and Cecil's normal attack, with a 50% damage bonus... and a 50% damage bonus to that if the target is a Machine. The only issue is that you need the Limit Ring to expose this (I've seen it do 20K with the Ultima Weapon+Thor's Hammer) and that to really benefit, the target should be a machine... but for 7MP, this is insane really (Rapid Ring v2 should help with the band and his speed). Unfortunately, this is affected by row (for both characters I think).

Calca and Brina are ultimate what Palom and Porom would be like if they were fighters... especially given the XP requirements for the dolls...
I have no idea why Harley gains the slowest levels... but surely she could cast some spells with whatever pathetic MP she has....
Cid's Risk Strike does force a Critical Hit (50% damage increase) but consider the following:
When the moon phase is beneficial, the damage dealt is almost 2 times his normal attack...
100 * 1.5 (critical hit bonus) * 1.25 (moon) = 187.5
Risk Strike is useful if you want to avoid HP or physical based counters.... because sometimes not killing the monster outright will get you killed (think Coeurls) or you simply want to avoid damage received by a counter...
Critical Hits happens only <5% of the time (maybe more), but this increases your chances to about 50%... so it's not as risky as it sounds.
Just simply DO NOT use it against monsters with the boss bit. It will fail all the time.
I will be looking into Palom's Boast vs monsters....

Also...
Jump and Focus actually doubles the attack power like before. I haven't looked into Human Kite though... critical hits don't increase attack power though.

I'm starting to think the RNG can be rigged like in the Wii port, but it requires either some thought to being quick and using multitarget spells or bands like Quake and occasionally some insanely damaging single target bands...