We have the ability to randomize/change who has what ability (including some that are not available on base characters). This changes the general power ranking of characters.
Morph - This ability is bonkers. Simply BONKERS. When used it doubles the damage you deal and halves the magic damage you take. You charge it up by fighting battles that give you magic points. This works on almost all spells, abilities, and broken rods etc. Spells that ignore defense do not have their damage doubled by Morph.
Shock - 128 magic power cannot be dodged magic attack that hits all enemies. This is really powerful and can be the main attack of the person who has it.
X-magic - This allows you to cast two spells in a single turn. Just like equipping the Gem Box. Without using a relic slot. This should also allow you to have the regular magic command if you need to use an esper or only cast one spell this turn.
Runic - Absorbs the next spell cast by anyone and gives the user MP. This ability can neuter some bosses entirely. It can absorb a huge amount of dangerous attacks. It is really good.
SwdTech - 1 - is a decent attack early. 2 - can trigger the psyco Cyan glitch (now able to be done by anyone who has SwdTech). 6 - is decent spread magic damage. 7 - Is Quadra Slice one of the better physicals in the game. 8 - Cleave is instant death to the entire enemy squad. Cyan's Dream will unlock all of the techs.
Throw - Not just a good way to use up all of the trash weapons you find during the game. It also ignores defense when throwing a regular weapon. Skeins are also about half powered rods and quite good, though they do use magic defense.
Tools - Auto crossbow is 125 physical spread damage decent for clearing trash mobs. Flash is 42 magic power based spread damage. Drill ignores defense and is a 191 base power attack. Chainsaw is 252 defense ignoring attack, but has a 25% chance to do an instant death attack. NoiseBlaster inflicts confuse. Debilitator adds a weakness to the enemy. Air Anchor makes it so the enemy instant dies on their next action, if they are vulnerable to instant death.
Blitz - generally good command with a variety of uses. Pummel, Aura Bolt, Fire Dance and Air Blade are fine attacks. Bum Rush is stupid good. Mantra can heal by the user’s current HP and heals status (namely Poison, Mute, and Blind).
Jump - A better attack. It removes the user from battle until they execute the attack making them invulnerable. It does 1.5X the damage with most weapons, and 2X the damage with a spear/lance. This is the same as equipping dragonboots. Dragon Horn makes the user hit multiple times.
Lore - This game’s version of Blue Magic/Enemy Magic. There are some really good spells, and some that are… well… useless. The option to allow anyone to learn Lores is a godsend to this ability and makes it much more likely to get good ones. Grand Train is best of course.
Blow Fish - guaranteed 1000 damage. Could be decent low level.
Quasar - 57 non-elemental power magic damage that ignores defense. Targets all enemies.
Grand Train - 84 power non elemental damage that ignores defense.
Aero - 125 power wind elemental damage to all enemies
Clean Sweep - 50 power water elemental damage to all enemies
Aqua Rake - 71 power wind/water damage to all enemies
Possess - Chance to remove the user from the active party, and instant kill the targeted enemy. Ignores instant death protection. Character will be on airship after the battle. This can be used on everything up to and including final Kefka.
Slot - can be a pretty consistent Chocobop/7-flush damage. Can do Joker Doom if the RNG is right. Can do Reverse Joker Doom any time.
Health - Free full party Cure 2.
Rage - Similar to Lore in many ways. Some are great and game breaking. Some are… crap. Top rages are below (and elsewhere in the guide). The learn after any battle flag in Alpha makes it much easier to gather more rages than vanilla.
Dance - It is uncontrollable, and the abilities can be randomized. It is unreliable, but can be powerful in the right circumstances. I am being generous with this rating. If the abilities are shuffled around it is very hard to use effectively as you do not know what will be used. Stumbles also severely hurt Dance's usefulness.
Capture - Steal and fight mixed. Meh.
Control - trade your turn for controlling an enemy. Can be decent but is too limited to be really good.
GP Rain - Damage is decent, but you usually have better things to spend your money on. It is non-elemental damage which can be meaningful.
Sketch - uses and random enemy attack, I don’t find this good outside of one hit killing Ultros 3.
Steal - can get some decent stuff, but I have not found it that useful.
Leap - I suggest turning on everyone learns flag which makes this useless.