I’m unclear on how much, if at all, the Antipathy/Sympathy spell charms the victim into not wanting to resist.
For example, if a wizard were caught in the spell and failed the save, could they recognize it as magic and attempt to dispel it?
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Failing the save means that the wizard is affected by the Antipathy/Sympathy spell. It's a very powerful (8th level) enchantment intended to cause revulsion or attraction, so that's what it does when it works. Until the affected creatures are no longer subject to the effects, they don't know that they're being externally affected. The Ending the Effect section states [emphasis mine]:
On a successful save, the creature is no longer affected by the target and recognizes the feeling of repugnance or attraction as magical[...]
The wizard, or anyone else, doesn't recognize that they're being controlled unless they succeed on their saving throw. (In my opinion, anything else is 'meta-gaming')
Unless a spell has a perceptible effect, a creature might not know it was targeted by a spell at all. An effect like crackling lightning is obvious, but a more subtle effect, such as an attempt to read a creature's thoughts, typically goes unnoticed, unless a spell says otherwise.
The spell has verbal, somatic and material components, and has a perceptible effect, an intense urge.
The spell is an Enchantment.
Enchantment spells affect the minds of others, influencing or controlling their behavior. Such spells can make enemies see the caster as a friend, force creatures to take a course of action, or even control another creature like a puppet.
Sympathy. The enchantment causes the specified creatures to feel an intense urge to approach the target while within 60 feet of it or able to see it. When such a creature can see the target or comes within 60 feet of it, the creature must succeed on a Wisdom saving throw or use its movement on each of its turns to enter the area or move within reach of the target. When the creature has done so, it can't willingly move away from the target.
The spell describes the effect, and how it impacts those affected. Creatures of the kind specified by the caster that are within line of sight or within 60' of the target must succeed on a Wisdom saving throw or suffer the consequences. Those consequences do not exceed those listed for the chosen aura.
If a creature fails the saving throw, that doesn't mean they do not understand they are under an outside influence. They feel the desire imparted by the spell, but are otherwise still in possession of their faculties. However, that knowledge only matters if they have a capability to thwart it. If a creature of the kind specified by the caster fails their save and the target does nothing to harm them, they may well be under the influence for 24 hours before they have an opportunity to make another save!