Modern science doesn't and cannot answer the endless debate of metaphysical preferences of your question, now as 300 years ago, you still can choose Newton's absolute spacetime or Leibnitz's relative spacetime.
Most people implicitly hold Newton's absolute spacetime view as there exists a permanent fixed background stage to start the motion stories, this is such a common experience and if you doubt about it seriously at the metaphysical level, you'll be regarded crazy everywhere.
But relativists like Leibnitz do hold a serious metaphysical ontological image which looks very different from the common. Like in pure clear Math, we require "same space" 3 attributes as follows as mentioned in @Conifold's SEP:
(i) A body comes to the "same place" as another once did, when it comes to stand in the same "relations" to bodies we suppose to be "unchanged".
(ii) Then we can define "a place" to be that which any such two bodies have in common.
(iii) space is all such places put together.
However, Leibnitz also holds that properties are "particular", incapable of being instantiated by more than one individual, even at different times; hence it is impossible for the two bodies to be in literally the same relations to the "unchanged" place. Thus the final "particular" nature of physical properties cannot satisfy requirement (ii) above. Obviously relativists regard "relations" between substances as fundamental properties of physical reality (ie, the definition of physical reality can only defined and thus measured via mathematical relations), just as a circle is NOTHING BUT a plane curve satisfying x^2 + y^2 = r^2 relation along its body.
In conclusion, just like there're no two exactly same leaves in this physical world, there're no two exact same background space when you are talking about different objects moving inside it. Of course, this doesn't mean in our ideal math realm there doesn't exist number "2" or any fixed unchanged space coordinate. The conflict is just the different metaphysical speculations of the underlying ontological world (assuming its existence), however, since metaphysics usually leads and creates any model or theory, the implications of them may be of huge differences...