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It is not necessarily true that Borel equivalence relations that are potentially in the same pointclass are Borel bireducible. For example, consider the orbit equivalence relations of the logic action of $S_{\infty}$ on the standard Borel space of torsion-free abelian groups of rank $n$. Then these orbit equivalence relations are essentially countable and hence are potentially $\mathbf{\Sigma^0_2}$ (for example, see this theorem). However, Simon Thomas proved that the Borel complexity of isomorphism of torsion-free abelian groups of rank $n$ (strictly) increases with rank (in this paper).