The size matters when the logo is going on the left chest. It should not be too big or too small.
The shape of the logo makes all the differences. If the logo is a circle, 2.5 inch will be the perfect size.
The business card size: 3.5x2 inch works perfectly. Usually Avoid 4 inches width or height or more for any logo going to a left chest.
It will be too big for your left chest shirt and also look out of proportion.
For Shirt with pockets, Logo are always place above the pocket not on them.
Large area embriodery on the bakc of Jackets or Hoodies is typically sized to fit within an area of 12"x 12" but sometimes depending your the customers need it can be smaller or larger.