Both the spigot and internal dovetail have their advantages, and disadvantages. Whether we use a spigot or a recess to hold the wood has nothing to do with one of them being "better" than the other. Which we use should be chosen from what we are turning, the wood that we are turning, and personal preference. Sometimes we choose one or the other because there is no other way to hold the wood.
I will describe my preferences for which one I would use and why. Someone else will have a different opinion.
a Spigot for a bowl with a foot
I prefer a spigot on the bottom of a bowl because the bottom foot can be turned to a smaller diameter than with the recessed dovetail. Sufficient wood has to be left outside the recessed area to absorb the expansion forces of the chuck, and this means that the base of the bowl will have to be larger than if it were gripped with a spigot. With a spigot the base of the diameter of the bowl can be turned to the same as that of the jaws as they are gripping on the spigot.
a Spigot for a bowl with a round bottom
If we are turning a bowl with a round bottom that has neither foot, flat spot, nor recess, the spigot may be the better way to hold the bowl. The final shaping of the bottom will only require removing the spigot and blending the curve of the bottom into the rest of the bowl.
a Spigot for the strength
The spigot can be the stronger grip because you can squeeze harder on a piece of wood in compression than you can pull on it in tension across the grain. I like to turn large pieces of wood, and a large and long spigot is the stronger way to hold a heavy piece of wood. Soft wood can be usually held with compression on a spigot with the aid of some CA glue, and there is often no way that it can be held by expansion inside of a recess.
Why not a Spigot
Some folks will advocate not using the spigot because of the wood that is lost. This loss of wood can be prevented when a waste-block is glued to the bottom of the bowl.
Weakness in a Spigot?
The only weakness in a spigot is when the wood has a flat grain that runs across the base of the spigot, and the wood is a species that splits easily. In that case it is possible to lose the bowl. Other than that one special case, I have never lost a bowl because of the spigot breaking, and I have lost a lot of bowls from break-out around a recess.
This break across the base of the spigot can be more of a problem with chuck jaws that have a "dovetail" profile, often called "smooth jaws", because if their wedging action at the bottom of the spigot. There will be less possibility of splitting if the spigot is tapered to match that on the inside of the "dovetail" jaw. This matching of the tapers will allow the jaws to squeeze on the spigot, rather than tey to pry it off of the bottom of the bowl.
When the Recess is better
The chucking recess is useful for turning plates and platters because it has the potential for wasting less wood, making it possible to turn a plate from a piece of 4/4 thickness lumber, and it is faster than gluing a waste-block to the bottom of the plate and then having to remove it. Keeping a large area outside of the recess isn't a problem with a plate or platter, the recess need be only 1/8" deep, and its bottom becomes a part of the larger recess when the bottom of the plate is finished.
The recess can also be the preferred way to hold a bowl with a smooth bottom that has no foot. There is usually no problem with having enough wood to support the gripping forces of the jaws.
Problems with the recess
We have already discussed the problem of not having enough wood around the outside of the recess to prevent the chucking forces from breaking the wood. Besides leaving more wood, the other solution is to use less force to hold the wood. Using a piece of pipe as an extension to tighten the chuck is not necessary, and will insure destruction of the wood.
The other problem with the recess occurrs because the recess is a subtraction from the outside of the form. Bowls can end up with bottoms that are either tissue thin or no bottom at all, and in the later case we call them a "funnel".
Other reasons to use a spigot or recess
There are those times when either a spigot or recess is used because that is the only way it can be done.
And there is nothing wrong with using either just because we like to do it that way.
How to cut the a spigot or recess
There are many ways to cut either a spigot or recess. I use a parting tool for making both, not that it is any better than another tool, but only because I have always done it that way. Others will advocate using a skew laid on its flat side, a spear-point scraper, a gouge, a skewed scraper, or any number of tools that will cut wood.
The dovetail shaped scraper is a relatively new tool for the woodturner who has everything else. I would use the money for some accessory jaws for that new chuck or a tool that is more useful.
However it is done, the conventional wisdom is that the profile of either the recess or spigot should be a close match with that of the chuck jaw. Straight spigots should be straight, and dovetails should match the dovetail. My personal preference is that angle in the wood should be offset just enough that the chuck will start to grip the top of the spigot or recess before the bottom.
How deep or how long depends on how much weight is being supported, and the personal "fear factor" of the wood coming out of the lathe while it is spinning. Personally, I make a 1/16" deep recess in a plate or platter; 1/16" less than the maximum the chuck jaws will accept for wood that is large, soft, or not round; and 1/4" deep or long for everything else.
