@Ryukan
So the point of AoO and Stand Still having both “move action”* and “leaves a square during a move action” is that “move action” one covers the moment a creature uses any action with the Move trait, including some actions that don’t leave a square (like the action Stand), and “leaves a square during a move action” covers cases where someone uses a Move action like Stride while outside your reach but then moves through your reach. Also note both of those exclude forced movement like being Shoved.
Both AoO and Stand Still are Reactions (they’ve got the looping arrow icon). The big difference between AoO and Stand Still is AoO triggering on Manipulate actions. Manipulate actions include all spells with a Somatic component (almost all 2- and 3-action spells) and Interact actions (like retrieving or using an item). However, do note that while critical hits with AoO disrupt Manipulate actions, critical hits with Stand Still dirsupt Move actions. So AoO can stop a spell cast, but Stand Still can force enemies to spend an extra action to complete the movement they were attempting.
My thinking is that AoO is clearly the better reaction but not by a huge amount. AoO will trigger off of movement the vast majority of the time, and triggering off Manipulate actions and ranged attacks really just forces casters and ranged attackers to eat the attack no matter what they do. Monks, if they invest in Athletics, can use Grapple to hinder spellcasters about as much as the chances of a disrupting AoO, and Monks have other options for messing with casters.
Also, Stand Still does not interact with your MAP from your turn. MAP goes away at the end of every turn, so you start with no MAP on each other creature’s turn. The text in AoO was probably just a reminder of that rule, but it actually has an interaction with some high-level Fighter feats that can let them use more than one AoO in single turn, which would normally incur MAP on the second and later ones. It could also benefit them in the extremely rare case of an enemy using a Reaction with the Move or Manipulate traits during the Fighter’s turn.
I will say, if you don’t plan to take any of the extra feats to advance an animal companion, it’s probably not worth trying to get. A better option might be for someone (like Rockie) to take the Bonded Animal skill feat and use that on the second Warg pup to get a “Helpful” animal buddy that will be willing to do things like low-threat scouting, tracking, etc (things that don’t put it in danger or cause it too much trouble). Just come up with whatever reason why one of them can’t/won’t fight (since the other one will be getting the progression feats, I assume).
And don’t make me go copy my gigantor post on Ranger stuff from a month back.
@ocelot
The problem with trying to get AoO on Valk (it is available as a 6th-level Champion feat) is that it competes with Retributive Strike for his Reaction, and Retributive Strike gives a little damage mitigation in addition to also making that Strike. So I just don’t see it being worth picking up for him. He’ll be taking Shield Warden instead, which is kinda useless at that level (it also competes with Retributive Strike for his Reaction, and it only offers a bit more damage mitigation in exchange for no Strike), but it’s needed for the ridiculous Shield of Reckoning at lv10. SoR lets him use Shield Warden and Retributive Strike as a combined Reaction. Levels 6, 8, 10, and 14 are where Valk will pick up the core of his build and turn into a bubble of “Hitting my allies will hurt you more than them”.
@Rando
I found another reason to be disappointed with Wizards. Every multiclass caster archetype has a Breadth feat that gives an extra spell slot of every level except your two highest. The Breadth feats for Sorcerer and Bard also add an extra spell to your Repertoire for each new slot added, so they get a bunch more spells known out of it. Does the Wizard one let you add any extra spells to your spellbook? Nope.
*They really should have decided on some textual mechanism to convey when they are using a word to evoke the trait with that name. The book never really clarifies that “a move action” means “an action with the Move trait”, even though that is apparently how they use it. Likewise with “attack action”.