These two approaches have big ramifications:
If you lead, you are always just a moment ahead, never slowing down too much, never waiting for them too much. If you follow the people singing, you first hear their voice, then play a note - this way it's always a little slower, always a little late.
In one church I played some 15 years ago, I used to lead but the congregation didn't want that. They were used to the dragging and extremely slow tempo where they would breath every two words or so. I guess they had their own notion that the congregational singing helps you go to sleep.
It was depressing. I didn't play in that church very long. Let them marinate without me.
But on the other hand, you can't always be too much ahead either.
It's a fine balance. A balance between picking the right tempo and performance.
Sometimes, you even have to sing yourself together with the people to help them sing better.
And of course registration. When you lead, the organ tends to play louder, doesn't it?
To lead or to follow? Here is a question.
PS Our choice reveals much more about us than just the hymn playing...
Diatonic Sequence in G Minor: iv-ii6-V-i