What does each Esper unlock on each board?
Based on the website RPGSite.net, the following is an extensive list of each Esper and which licenses they unlock for each job. The website also gives suggestions on which options provide the most benefits based on different combinations, but the decision is ultimately up to you
Belias, the Gigas
Knight: Potion Lore 1
Foebreaker: Horology technick
Bushi: Libra technick
Suggestion: As Belias is the first Esper in the game, his License Board unlocks are not great and will not add much to your skillsets. Libra is found in many other classes already, and Horology is an awkward Technick based on your game clock, so Potion Lore 1 is our best recommendation.
Adrammelech, the Wroth
White Mage: Souleater technick, Battle Lore
Uhlan: Battle Lore
Time Battlemage: Cura, Raise magicks
Foebreaker: Battle Lore
Black Mage: Fumarole, Tumulus equippable
Bushi: Souleater technick
Shikari: Shades of Black technick
Suggestion: There is no obvious pick here. Time Battlemages do not get access to White Magick otherwise, so giving them Cura and Raise could be useful in a pinch or some additional healing. An extra Battle Lore for you Foebreaker or Uhlan never hurts. Hand Bombs on your Black Mage is probably only useful in very specific builds. Consider if you have a character that can benefit from Adrammelech twice, such as an Uhlan/Time Battlemage.
Zalera, the Death Seraph
Monk: Traveler technick
Time Battlemage: Ether Lore 3
Foebreaker: Traveler technick
Black Mage: Steal tech, Poach technick
Bushi: Blood Sword, Karkata equippable
Shikari: HP+435
Suggestion: Traveler deals damage based on the number of steps you've taken since you last used it - not very useful. Having another character able to Steal isn't useful either. HP+'s aren't as valuable in late-game because Bubble will likely bring your character to 9999 HP regardless. We suggest going with Bushi for additional access to weaponry or Ether Lore for your Time Battlemage. (Blood Sword causes Sap and Karkata causes Confuse on hit)
Cúchulainn, the Impure
White Mage: Libra technick
Uhlan: Wither technick
Machinist: Magick Lore
Red Battlemage: Firaga, Thundaga, Blizzaga, Sleepga magicks
Knight: Battle Lore
Foebreaker: Shades of Black technick
Bushi: Stamp technick [Also unlocked by Ultima]
Shikari: Protectga, Shellga magicks
Suggestion: The most enticing selection here is more Black Magick for your Red Battlemage. If your Red Battlemage is also your Black Mage (and thus already has those magicks), then we suggest giving Cúchulainn to your Shikari for additional protective buffs.
Mateus, the Corrupt
Uhlan: Magick Lore (x2)
Knight: Curaga, Esuna, Cleanse, Regen magicks
Time Battlemage: HP+230
Black Mage: Caldera, Volcano equippable
Shikari: Gil Toss technicks
Suggestion: Knights do not gain access to White Magick on their own, and another character able to use Esuna/Cleanse/Regen is probably your best option (unless your Knight is also your White Mage). Gil Toss has its uses, but you probably have plenty of characters who can do that already. The HP+ node is there if nothing else is valuble to your setup.
Exodus, the Judge-Sal
White Mage: Battle Lore
Machinist: Oil, Decoy magicks
Red Battlemage: Platinum Helm, Giant's Helm, Dragon Helm, Platinum Armor, Carabineer Mail, Dragon Mail equippable
Knight: HP+350
Monk: Souleater technicks
Time Battlemage: Battle Lore
Foebreaker: Magick Lore (x4) [Also unlocked by Zeromus]
Black Mage: Platinum Helm, Platinum Armor equippable
Shikari: Stamp tech
Bushi: HP+500
Suggestion: There is no clear winner here. All those heavy armors for your Red Battlemage look enticing, but for end-game purposes, they probably aren't going to be as useful as high-end robes. Still, other options are not much better. The 4 Magic Lores are worth a look if your foebreaker is also a mage and does not already have access to them. As always, consider if you have any job pairings that can benefit from Exodus twice.
Zeromus, the Condemner
White Mage: HP+270
Machinist: Makara equippable
Red Battlemage: Channeling
Monk: Sight Unseeing technick
Time Battlemage: Addle technick, Shear technick
Foebreaker: Magick Lore (x4) [Also unlocked by Exodus]
Black Mage: Giant's Helm, Carabineer Mail equippable
Bushi: Magick Lore (x2)
Suggestion: Channeling reduces MP cost by 10%, and that's a good thing for your Red Battlemage to have (especially if you gave them Cúchulainn for higher level Black Magicks). Otherwise, Addle and Shear are especially good debuff technicks you can give to your Time Battlemage. Bushis already get plenty of Magick Lores, but they can get two more if you choose. Plenty of good options here.
Chaos, Walker of the Wheel
White Mage: Defender, Save the Queen equippable, HP+310
Uhlan: Aeroga, Bio, Blindga, Silencega magicks
Machinist: HP+350
Red Battlemage: Ultima Blade equippable
Knight: Excalipur, Revive tech, HP+390 [Also unlocked by Zodiark or a Quickening node)
Monk: Esunaga, Protectga, Shellga, Holy magicks
Time Battlemage: HP+270
Archer: Magick Lore
Bushi: Brawler
Suggestion: If you have a Black Mage/Monk, give them Chaos for sure. Holy will be a very useful spell to have and the protective buffs are just a bonus. These are good magicks for your monk to have even if they are not also a Black Mage. Otherwise, the next best options is probably the Uhlan support spells or giving greatswords to your White Mage.
Shemhazai, the Whisperer
White Mage: HP+230
Machinist: Caldera, Volcano
Red Battlemage: Cleanse, Esuna magicks
Knight: Potion Lore 2
Monk: Potion Lore 3
Archer: Dragon Helm, Magepower Shishak, Grand Helm, Dragon Mail, Maximilian, Grand Armor equippable
Black Mage: Steel Mask, Mirror Mail equippable
Bushi: Shield Block
Shikari: Spica, Antares, Arcturus, Fomalhaut equippable
Suggestion: Giving Shemhazai to your Archer will allow them to wear the best heavy armors in the game. Giving your Red Battlemage status removing skills will also be sure to come in handy. If your Red Battlemage and your Archer are the same character, then this is an easy choice to make. None of the other selections come close.
Ultima, the High Seraph
Uhlan: Expose technick
Machinist: Magick Lore (x3) [Also unlocked by a Quickening node]
Red Battlemage: Claymore, Defender, Save the Queen equippable
Knight: Telekinesis tech, Battle Lore
Monk: Swiftness (x2)
Time Battlemage: Diamond Sword, Runeblade, Deathbringer, Stoneblade equippable
Foebreaker: Swiftness
Archer: Infuse technick, 1000 Needles technick [Also unlocked by Zodiark]
Black Mage: Telekinesis tech
Bushi: Stamp tech [Also unlocked by Cúchulainn]
Shikari: Phoenix Lore (x2)
Suggestion: Swiftness is the best passive node in the game (reduces action by 10%). If your Monk does not already have Swiftness, then give them Ultima. If Foebreaker needs the Swiftness, then give them Ultima. If both your Monk and Foebreaker already have Swiftness, then the next best option is probably Expose for your Uhlan. As always, see if you have any characters that can 'double benefit' with Ultima.
Zodiark, Keeper of Precepts
White Mage: Claymore equippable
Machinist: HP+390
Red Battlemage: Ragnarok equippable
Knight: Excalipur, Revive, HP+390 [Also unlocked by Chaos and a Quickening node]
Monk: Renew Magick
Time Battlemage: Durandal, Simha equippable
Archer: Infuse tech, 1000 Needles tech [Also unlocked by Ultima]
Bushi: Giant's Helm, Dragon Helm, Magepower Shishak, Carabineer Mail, Dragon Mail, Maximilian equippable
Suggestion: Zodiark mostly adds high-level equipment to classes that could not otherwise wield them. Renew is the highest level White Magick that fully heals your team but it is costly to cast. For Zodiark, it is probably best just to see which characters can double up best on the unlocks he provides.
Hashmal, Bringer of Order
Uhlan: Bonecrusher technick
Red Battlemage: Steal technick
Knight: Curaja, Bravery, Faith, Confuse magicks
Monk: Cura, Raise magick
Time Battlemage: Channeling
Foebreaker: Swiftness
Black Mage: Makara equippable
Shikari: Bonecrusher technicks
Suggestion: Like Mateus, it is probably best to give Hashmal to your Knight in order to give them some White Magick abilities. If your Knight is also your White Mage, then the next best choice is probably Channeling for your Time Battlemage.
Famfrit, the Darkening Cloud
White Mage: Orichalcum Dirk, Platinum Dagger, Numerology technick
Uhlan: Potion Lore 3
Machinist: Hastega, Slowga, Vanishga, Reflectga, Warp, Graviga magicks
Red Battlemage: Battle Lore (x2)
Monk: Arise, Dispelga spells
Time Battlemage: Battle Lore
Foebreaker: Magick Lore
Archer: HP+390, HP+435
Black Mage: HP+190, HP+230, HP+310
Suggestion: That's a lot of useful Time Magicks you can give to your Machinist, so that's probably your best bet. Even better if you have a Machinist/White Mage.