Capturing a monster will always give you more rewards but sometimes also different ones. Personally I'd say capturing a monster is "better" unless you're farming for a very specific item that can only be carved. You can see the rewards of monsters in your hunter's notes and if a certain Item only shows up in the "Carving" tab you won't get it from capturing a monster.
As a quick list: Here are some pros and cons for capturing a monster in MH World.
Pro
- More rewards than from killing a monster
- Only 20 seconds to return to camp/HQ (the hunt is faster in general)
- You can usually get "breakable" items even though you didn't break the part of the monster (Tails if you're using a blunt weapon for example)
- Gives you more research points than simply killing it.
- Messing up a trap isn't as bad anymore since you can restock everything in your tent.
Con
- Requires some setup (Traps, Tranquillizer)
- Requires precision and Knowledge of the monster (When can you capture it?). When normally hunting a monster you can just smash it without much thought about when to stop.
- Some Items may be carve-only (From personal experience Plates, which are very rare, have a higher droprate in carves than in quest-rewards but I don't have any numbers on that)
- The monster needs to be lured towards a specific location. Traps don't work everywhere.
In general I'd say you should capture monsters if you're farming for a specific armor set and if you're still missing some specific items you can go for a normal hunt (only if the drop chance from carving is better of course).