What is the difference between the recoil from a normal and a magnum cartridge?
If you only compare the recoil energy, then it is easy. A .30-06 with standard load and 11.7 g bullet produces energy of 30 J, while a .300 Win Mag with the same bullet but 915 m/s produces energy of 44 J. A .378 Weatherby generates 95 J and a large cartridge such as the .505 Gibbs 149 J.
The recoil felt depends on how fast it comes and on the weight of the gun. Most people feel that the recoil from a .378 Weatherby is greater than from a .505 Gibbs because of the bullet weight and velocity. You can however effectively reduce the recoil with a good, wide butt plate and a straight gun stock.