What would be the difference when I see lathe chucks offered and some are 4 jaw and some are only 3 jaw. Difference in holding power? Is less putting more pressure on each jaw or does the greater surface of 4 increase friction on the part being held?

I have both 3 and 4 jawed chucks. I use the 3 jawed pretty much now only when I'm doing certain things on cane rods. since the rods are 6 sided the 3 jaw works best there. however, for most other operations I use a 4 jawed. I started out withthe Wood River 4 jaw from Woodcraft and bought the extra smaller jaws for it. now that is what I use 90% of the time. works reall great for holding mandrels reel seat inserts etc.
Hope this helps.

When turning mandrels and other round objects, 3 jaw is fine. FOr turning/boring square stock, you need a 4 jaw.

Be careful as some 4 jaw chucks have independent jaws. These are used primarily on machine lathes where you have to manually center out of round objects. Most chucks sold in woodworking stores, however, are self centering scroll type chucks. Just make sure you know what you're buying.

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James,
Best to have one of each.
Then, when you are on symmetrical objects you can use a 3 jaw chuck.
If the object is not symmetrical you can use the 4 jaw chuck.

Chucks like Taig 3 and 4 jaw chucks are both self centering. So, one twist of the back plate will tighten up either chuck.

Some folks like to use the 4 jaw chuck better because there is slightly less pressure per chuck to hold the object in place.

If you do have a chuck with replaceable jaws and intend to hold rod handles, it is nice to have one set of jaws that have an inside concave that will roughly match the outside taper of the typical 1 to 1 3/4 inch rod handle. By having an inside concave shape on the lathe chuck jaw, the jaw will hold many times better than a flat jaw. The flat jaw only touches the handle in an area about 1/16th of an inch wide. But a concave jaw will have a contact area that is equal to the width of the jaw which may be up to 3/4th of an inch.

One example of a Taig 4 jaw chuck using the soft aluminum jaws which have had an inside concave shape ground into the face of the jaws:

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I have had a self centering 4 jaw for years and it is all I have used without issue. If I am using a mandrel I prefer a jacobs therefore you never have slip.

Eric,
X10 on your use of a jacobs chuck when using a solid rod for anything in the lathe. Excellent grip and perfect stability witth the Jacobs chuck.

Roger

Another good option when using mandrels is, a collet chucking system. Collet's grip the mandrel firmly and smoothly (no marring of the mandrel). The ability to slide the mandrel into the collet for any length is another advantage.