Jumping saddles are very different to dressage saddles. They are made to put the rider in a completely different position. A well made, quality jump saddle puts the rider in a better position. This offers more security for the rider over jumps then a saddle designed for flatwork.
The jumping position started with a french cavalry officer, Federico Caprill. Federico taught his pupils to ride over jumps in a forward position with shorter stirrups. This centred the riders weight and allowed the horses to jump more freely.
The forward cut flaps allow the rider to shorten their stirrups and bring their knees up higher. The flaps are also shorter so the rider can get closer contact with the horse.
Modern show jumping saddles have kept to this classical ideal in their saddles, while introducing innovative technologies to constantly improve this experience.
Brands such as Prestige and Pessoa are the forefront in this innovation. https://www.lanoirsaddleworld.com.au/brand/prestige-saddles/