Instance, not static
For this case I think the second choice is clearly better. If you think about it, any method could be implemented as static if you are willing to pass the object to it, this only seems to be a special case because the other parameter is also an instance.
Therefore, our search for symmetry and abstraction is slightly offended by having to choose between the two instance objects for the dot operator. But if you look at .method as . then operator, it isn’t really a problem.
Plus, the only way to do functional-style chaining is with an attribute, i.e., instance method. You probably want thing.up.down.parent.next.distance(x) to work.