width / board performance...

how does a board’s width affect its overall performance, taking into account things like sensitivity, control, responsiveness, turning radius, down the line speed (vs. drag), etc. i.e. if i ride a narrower board than the 20 1/4 inch wide 6’6 i am riding now, will it help me get to where i want in surfing (which is a progression towards increasingly powerful, vertical, and smooth turns, and overall more control and a looser feeling) ? granted a LOT of other factors come into play here but just as far as board width, what does a narrower board do vs a wider one?