A rolling stone gathers no moss but a rolling oak smashes your berries and face.

Oak log, or as a geometric object, a solid cylinder.

A sphere only has one contact point with the ground, which means all it's weight is concentrated onto one point, which increases the pressure on the ground and the sphere, which could cause deformation, depending upon the ground and sphere. While a cylinder has it's weight better distributed along it's axis, reducing pressure.

Having more contact with the ground also reduces occurrences of slipping, which is usually undesirable for "perfect rolling." A solid cylinder does have a higher moment of inertia (assuming the sphere is the same mass and density), which means it takes more energy to get it rolling, which may be bad, but the higher energy also means it will roll longer than a sphere, since each will experience the same frictional force, but the cylinder will have more energy that friction has to take away before it stops rolling.

In short, there are reasons why tires are not spheres, but cylinders.

I would say, in a ideal setting, the perfect sphere would roll better, but in Valheim, where there is a natural attraction between logs and your head, the edge goes to the logs.

The build/no spawn radius around the center of a workbench in Valheim is a perfect sphere. I have never seen that perfect sphere roll at all. I have seen logs of all species of trees which can be chopped down roll in Valheim.

I have to say that logs roll better than perfect spheres.

Perfect spheres only roll better on perfect slopes. The large round oak log will ignore minor speed bumps like the player and keep going.

Depends on material of the sphere. I'd expect the odds to get pretty even between oak log and oak sphere, but the initial conditions can make a difference too, like if the oak was split into logs mid-air or on the ground.

Does it make a sound when you aren't there to hear it though...

is the moon still there when no one looks at it?

those question are just a waste of time