Not sure what do you mean by rich sound but anyhow,let's talk about pickups.

As you know,pickup is there to collects string "ringing" and sends it to amp,preamp or whatever.
If it has high output you'll send higher sound/signal to amp and opposite.
So it's actually a transmitter BUT it has some dealing with the tone of course.
Each pickups has its own character and it's important to match it right with your guitar.
Moody and bassy PUS wouldn't go nicely with mahagony body etc...
When you define character you wont,then you're on to output.
It's actually mater of thaste,just like everything in art such is music.

Some players need more output for legato runs,
while vintage players like midrange output,feels more natural to them.
And of course,less gear you have,pickups is more important.
More gear you have,pickup is less important but still transmits the sound so have that in mind.