Gantry shear is primarily used for cutting thick metal, while box shear are mainly used for cutting thin metal.
Here are the difference

Structural:
Gantry shear :
Open-cut design, typically equipped with a long conveyor feeding , or chain plate feeder
Box shear :
Fully enclosed or semi-enclosed hoppers with built-in pre-compression functionality
Functions:
Gantry shear :
Shearing (cutting cleanly, like with scissors)
Box shear :
Pre-compression + shearing (first compacted into a block, then pushed out and sheared).
Apply:
Gantry shear :
Heavy and long scrap steel (such as I-beams, rails, thick steel plates, and large-diameter rebar)
Box shear :
Lightweight, loose scrap metal (such as color-coated steel roofing sheets, car bodies, bicycle frames, and metal drums)
Operating Methods:
Gantry shear :
Suitable for cutting long, continuous materials; typically used in conjunction with an automatic feed table
Box shear :
Ideal for bulk feeding and processing by the box, suitable for handling mixed scrap materials
Safety:
Gantry shear :
The cut edge is open and requires the use of photoelectric safety guards; its resistance to flying debris is relatively weak.
Box shear :
Fully enclosed operation keeps sparks and debris contained within the housing, ensuring greater safety
Mobility:
Gantry shear :
Most are stationary, bulky, and require a foundation
Box shear :
Many models are designed for mobile use in vehicles, requiring no foundation and making relocation easy.