When considering which mesh setup is better for joints, it is important to focus on how well the mesh can maintain volume and avoid deformation during movement. The first image, which is stretched radially around the joints, may provide better control over the joint area, allowing for smoother bending and less volume loss. This is because the radial arrangement can help distribute the deformation more evenly around the joint. The second image, which splits the mesh in straight lines, might be simpler but could lead to more noticeable deformation at the joint due to less control over the vertex distribution. Ultimately, the choice depends on the specific animation requirements and the complexity you are willing to manage.

rmx This is just an example from my own experience, but I often take the approach of setting the vertices radially, similar to the first example you mentioned.
The reason is that, as shown in your screenshot, there are often shadowed areas where a radial layout tends to create smoother connections.

On the other hand, in one of the official example skeletons, mix-and-match, the vertices are connected in a straight line, similar to the second example you mentioned:

In this skeleton, the arms and legs are designed to bend in a rounded manner, so connecting the vertices this way makes sense:

As Spinebot mentioned, the appropriate way to set up vertices and edges depends on the kind of movement you want to achieve, so it’s difficult to give a one-size-fits-all answer.

I hope this helps in some way!

rmx Experience tells me, if the join has to be rigid, the best option is two separate images with an overlapping pivot (the rounder the better). If that's not possible, first option can make the cut but not at an extreme overlap.
If the joints have to be soft and bendy, then parallel lines are quite useful.
We discuss mesh structures in this article:
https://esotericsoftware.com/blog/a-taxonomy-of-meshes