Ranking from the most to the least:
Embroidery > Screen Print> Heat Transfer Print> Gold foil print and Silver foil print
It is because the color threads is embroider onto the clothes, logo fastness for Embroidery is the best. Screen Print is the most common logo printing method, logo fastness of the paste is also good on fabric. For Heat Transfer Print, as logo is printed on clothes by heat, logo fastness is also quite good. But for Gold foil print and Silver foil print, as there are restrictions on foil material, slight discolor and logo peel off will be found after washing for a period of time. However, proper garment care should always be applied in handling the garment. Even with the best colorfastness logo, if daily wearing and washing are mistreated (e.g. ironing on the screen print logo will result the print material to melt), it will not help to maintain the garment in good shape and wearable conditions.