It depends. The answer to what's the "right" way to do things depends on what you need. Obviously, one of the components to determining what's right is how much time it takes to do-- and doing your top, triangulated mesh takes very little time.
But doing the bottom, quad only mesh is superior for several reasons, that may or may not matter for your actual use:
The base meshes, with autosmooth at 90 degrees, are fine. There's nothing wrong with the lazier mesh. It has a few more vertices than the quad mesh, but then, it has more detail than the quad mesh. It's important to notice that all those triangles are planar with each other-- basically, we're using autosmooth to separate the questionable components of our triangulated mesh to a single, flat-shaded plane, so the way our normals interpolate across the triangles doesn't matter.
But with subdivision, we see that the triangles aren't subidividing in the way we probably want. Our quad mesh is smoother than our mesh that uses triangles.
In a fully smooth shaded mesh, we can see that the normals don't change evenly. Where we have the tightly packed triangles, the normals change rapidly. We can see the triangles if we look for them. Again, our quad mesh is smoother, even with fewer vertices.
In our mesh with vertex color, we can again see that the vertex color doesn't change as evenly across the triangle mesh. Even with fewer vertices, our quad mesh interpolates these values more properly. (Which shouldn't be surprising, given what we saw for the smooth shaded normals-- vertex color and smooth shaded normals are both interpolated the same way, as is UV or any custom vertex data.)
So if you're not subdividing, and you're not using vertex color, and you're not using smooth-shaded normals across non-planar elements, and you're not replacing your smooth shaded normals with a normal map, or maybe if you're using a material that doesn't even care about normals like emission-- then there's nothing wrong with the triangulated mesh. So the fact that it's easier makes it better. But if those things aren't true, then you're likely to run into rendering artifacts that you don't want with the triangulated mesh, and then the quad mesh is preferable.
Note that deformation can affect this, but it can affect this both ways-- sometimes, you'd rather have triangles for animation, and sometimes, you'd rather have quads for animation.