Thesis: Even though Platonists and Aristotelians can have the same metaphysics of the Trinity, nonetheless it is harder for the Platonists to distinguish the doctrine of the Trinity from tritheism. But the Christian Platonists can still escape the charge of tritheism by accepting divine simplicity.
I shall assume that Aristotelianism accepts individual forms, so that the humanity of Peter and the humanity of Paul are numerically distinct. If it turns out that Aristotle did not accept individual forms, then I shall not deem Aristotle an Aristotelian.
Now I can argue for my thesis. Take the same metaphysics of the Trinity: There is one divinity and three hypostases (subjects, persons, individual substances, etc.). Each hypostasis has the numerically same divinity.
Suppose Platonism is true. Then the Trinity is analogous to three human beings, say Socrates, Plato and Aristotle, each of whom is a distinct hypostasis that has the numerically same humanity. Indeed, if the human ousia is humanity, then Socrates, Hypatia and Catherine are homoousioi, numerically one in ousia.
Suppose isntead Aristotelianism is true. Then the Trinity is no longer analogous in this way to Socrates, Plato and Aristotle, because Socrates, Plato and Aristotle have numerically three humanities which are numerically distinct. Socrates, Plato and Aristotle are only homoiousioi, alike in ousia.
Now insofar as the Trinity is analogous to Socrates, Plato and Aristotle, thus far the doctrine of the Trinity is like tritheism. Hence, if Platonism is true, the doctrine of the Trinity is more like tritheism than if Aristotelianism is true.