Capturing ends the hunt sooner and unlocks its own reward pool, but a few materials — tail carves included — only ever drop from a kill, and a handful of monsters won't let you capture at all.
Capturing ends the fight the moment a weakened monster is trapped and tranquilized, instead of fighting it all the way to zero HP — it's faster and just as rewarding in its own way, but it trades away the carving you'd get off a corpse, tail included. Which one's actually better depends entirely on which material you're after, not on which feels more "complete."
Capturing takes two things sitting in your pouch before the fight starts: a trap and a tranquilizer. Neither works until the monster is already beaten down, so the sequence is always the same:
Shock Traps and Pitfall Traps both work, but they're suited to different monsters: a trap that a monster shrugs off once won't catch it a second time in the same fight, so it's worth carrying one of each rather than committing to a single type. You can technically set a trap the second a hunt starts, but it won't do anything until the monster is actually worn down — traps and tranquilizers only take hold once the fight has reached that late stage.
You don't need to stare at a health bar you can't see to know a capture is on. Watch for:
Any one of these is a reasonable signal to start setting up; the skull icon is the one to trust if you only check one thing.
Both endings hand you quest rewards and standard target materials — capturing doesn't shortchange you on the baseline rewards for finishing the hunt. Where they diverge is in the extras layered on top:
So the actual decision isn't "which is generally better" — it's "which material am I hunting this monster for," and whether that material lives in the capture pool or in the carve pool.
Quest text settles this before you even load in. A quest that explicitly calls for slaying a monster won't complete if you capture it instead — the objective just doesn't register. Some quests go the other way and specifically want a capture. Outside of quest wording, a handful of monsters simply can't be trapped and tranquilized at all: elder dragons are the broad category guides agree on, and Zoh Shia specifically is called out as impossible to capture under any circumstance. Everything else eventually goes down to a trap once it's worn out enough, even monsters that shrug off a given trap type early in the fight.
By the time you're staring at a beaten, limping monster with a skull icon over its head, the decision should already be made — check what the quest requires, and check what you actually need from this specific target before you commit a trap. If you're farming a tail carve or a post-kill material, keep fighting. If you're after a capture-only reward, or you just want the hunt over with less risk to your own health bar, set the trap. Either way, knowing which weapons and items you're carrying — traps and tranquilizers included — before the monster even limps is what makes the choice a real one instead of a scramble. None of this touches how often your hits land as crits along the way; that's a separate question, covered in what affinity actually does.