TL;DR for the Exemplar

The Exemplar is a strange beast. They're a martial that echoes power from stories and mythology, so their powers are reminiscent of Greek Heroes or Knights of the Round Table (even the flavor text says you may have drawn a weapon from a stone). Their gimmick is that they have a 'divine spark' that they can move between Ikons (representations of their divine power). Ikons can be part of their body (the face, the skin, a scar), a weapon, or a worn item - an Exemplar gets one of each type. In general: Body Ikons grant self-defensive abilities, Weapon Ikons grant offensive bonuses, and Worn Ikons grant auras that support allies.

While an Ikon holds the divine spark, it grants both passive benefit and access to a 'Transcendence' action. A Transcendence action is a powerful effect based on the Ikon, and after resolving the action the divine spark is forced to jump to a different Ikon. So the Exemplar is effectively playing a juggling act where they're constantly weighing the benefits of which passive Ikon effect they want vs the Transcendence action they're setting up for.

Some example Ikons: Gaze as Sharp as Steel (Body) - Passive: +1 Perception and +2 AC vs ranged attacks. Transcendence: Gain Reactive Strike feat for the round Scar of the Survivor (Body) - Passive: +1 on Fortitude saves. Transcendence: Heal 1d8 Hit Points (scaling with level) Yes, this allows effectively infinite out-of-combat self healing Barrows Edge (Sword-like Weapon) Passive: 1 Persistent damage on a Strike. Transcendence: Gain HP equal to half the damage it just dealt Fated Shot (Projectile Weapon) Passive: +1 damage per Strike. Transcendence: Can strike a 5-foot burst with a hail of projectiles. Victor's Wreath (Worn) Passive: You and all allies within 15 feet get +1 to attack rolls. Transcendence: Allies may immediately make saving throws (with a +2 bonus) to end ongoing conditions

As an Exemplar levels, they acquire additional abilities for their Ikons. (free actions with their Body Ikons at level 3, critical effects and alternate damage types for Weapon Ikons at level 7, and additional range and ally buffs for Worn Ikons at level 15). They also have the ability to 'reassign' Ikon status to new objects of a similar kind - so if they find a magical bow, they can make that their Ikon of Fated Shot for example.

Exemplar feats include some options for increasing offensive power (new weapon traits, bonus damage, alt damage types), physical utility, durability, and divine focus spells. There's a very fun one at level 4 called Only the Worthy, where you can command your worn or weapon Ikon to remain motionless - potentially pinning down a prone enemy or blocking a door - the feat also allows you to call the Ikon back to your hand.

TL;DR for the Animist

Flavor-wise, the Animist is a cross between a Druid and a Summoner. They call upon the spirits of the land, whether those be humanoid ghosts, animal spirits, or anthropomorphized versions of the land itself.

Apparitions: The main gimmick of the Animist is that each day during their preparations, they call upon a number of apparitions to be bound to them for the day. (2 at level 1, 3 at level 4, and 4 at level 12). The Apparitions grant 2 Lore skills each, these lore skills are relatively limited - being almost entirely terrain based (Mountain Lore, Forest Lore, etc.), although there is a Battlefield spirit that can be called to grant Battlegrounds and Heraldry Lore.

Spellcasting: They're divine prepared spellcasters, but they only prepare about half of their spell slots per rank. The other half of their spell slots are determined by the apparitions they've summoned that day. For example, calling a Volcano spirit and a Forest spirit would give the Animist the option of using Fireball or Wall of Thorns for their 3rd level slots (determined at time of casting). Each spirit also grants access to a Focus spell.

At first level, they can get the feat Channler's Stance - while in the stance, they add the spell's rank to any energy damage done by the spell - which I imagine will make them fairly proficient blasters.

Feats: Animists have feats that give them bonuses when dealing with undead and spirits (both in combat and socially), they have a few metamagic options - though these differ slightly from the standard set that other spellcasters have, abilities that allow them to resist or outright ignore mind affecting conditions on themselves, abilities that boost their melee damage and durability, and a couple abilities that boost their spell damage output.

Shout out to the 4th level metamagic feat Grasping Spirits - where instead of extending the reach of a spell, you send out an apparition to grab your target and pull it into your spell's range. (If the pull fails, you waste your spellcasting actions but keep the spell slots/focus points)

At 12th level, they can take feats that allow them to force a d20 reroll once per 10 minutes under certain conditions. (Would be spotted during stealth, ally would miss an attack, animist would be hit by an attack)

All-in-all: Their grab-bag of abilities feels pretty underwhelming, which is pretty normal for a spellcaster. Consistent damage output from spells and a near immunity to mind control effects is their bread and butter. The melee damage bonuses feel like trap options, since they only have simple weapons and they don't get nearly enough melee effects to make Strikes seem worth it. Medium armor proficiency gives them some durability, but that's about the extent of their protection. They get powerful Avatar forms at level 19, but that happens so late in the game I doubt many will ever see it.