What are the benefits of the different cylinder caps? I've been modeling for quite some time but I’ve never bothered to ask this question.

There are several ways to subdivide a cylinder cap? I've been going across vertex to vertex (right example), but I’ve seen a great many models and more experienced modelers triangulate along the perimeter (left example). What are the benefits of triangulating the edges as opposed to cutting it across, triangulating to a center vertex or just leaving an N-Gon?

I suppose once the object is triangulated (in a game engine like Unity or Unreal), the way I’ve been doing it would lead to one extra polygon on the cap end. Is this the reason the crossing rectangles approach isn't used as much?
I like the topology clean whether it's game model or not - so here are all the caps you will ever need:



If you have more sides, you can downscale these caps into them - the corresponding sub-cap topologies are highlighted (4-side cap, 6-side cap, 8-side cap):



With this you can make very clean any size cap with grid-like topology (which is very good).

If the number of sides is too big, the marked quads on next example will be a problem. This is how to setup loops in such topology to keep it again mostly grid and fix the problem:



Not only for subdivision topologies it's always good to inset the cap like so (its good for smooth shading also, thus for normal-maps etc.):





I don't like the square approach for triangles, I would prefer the vertex-to-vertex quad approach if I had. Long thin quads are bad also but still better than triangles.

Creating a triangle fan could be only pardoned in mobile game models or when flat shaded. Long thin triangles and a vertex with more than 5 edges are both the worst from topology and shading standpoint.