One of the easiest and most dramatic changes you can make to your banjo tone is to change where you pick the strings in relation to the bridge. This holds true for all stringed instruments. The closer to the bridge, the brighter yet thinner sound you will get, while the farther away you move from the bridge, the thicker and warmer tone you will have.
When you play different styles of music, take a solo break, or are comping chords, you might want a different tone and thus would move to a different location on the strings for picking your banjo. For example, most traditional bluegrass banjoists prefer a bright, crisp tone when taking a lead break. This allows them to cut through the rest of the band. When these banjoists are playing backup chords though, they will usually move their hand closer to the neck in order to have a warmer tone and blend in more.
Many clawhammer players go as far as to play above the fingerboard. Their banjos often are built with a scoop in the neck (the last 5 frets or so are pulled out and the fingerboard is carved out some) so that they can play above the fingerboard without hitting the frets. By playing above the fingerboard they are playing very far from the bridge and closer to the center of the string (between the bridge and nut) where the string tension is at its loosest. This gives them a very warm and fat tone. This type of tone is often preferred by old time style banjoists.
4 string jazz banjoists will change their position often based on the type of song, or if they are picking single notes or strumming chords. There is no hardened rule as to what to do, but again, if they want a bright tone that will cut through, they will play close to the bridge. If they are looking for a fatter, warmer tone, then they will play over the head and closer to the neck.
Electric guitars that have multiple pickups in them have these multiple pickups there, often one by the neck and one by the bridge, for the same reason. The neck position pickup will give a fatter and warmer tone while the bridge position pickup will be brighter and cut through more. What to use really depends on the musical situation and the player's own taste.
Again, there are no hardened rules. Try playing in different positions and notice the change in tone. Figure out what musical situations you will want to be playing in specific positions. Go with what your ear tells you to do.