There are many differences, including acceptance criteria for RT, MT and PT. Hydrostatic test and pneumatic tests have different criteria.
You need to read and understand both Codes.
B31.3 addresses impact toughness requirements for materials and welding procedures while B31.1 does not.
The primary purpose of B31.1 is to provide safety in design of pipe systems carrying water and steam.
B31.3 deals with all manner of fluids in addition to water and steam - toxic, flammable, highly corrosive chemicals, etc.