  Given a countable o-minimal theory T, we characterize the Borel complexity of
isomorphism for countable models of T up to two model-theoretic invariants. If
T admits a nonsimple type, then it is shown to be Borel complete by embedding
the isomorphism problem for linear orders into the isomorphism problem for
models of T. This is done by constructing models with specific linear orders in
the tail of the Archimedean ladder of a suitable nonsimple type.
  If the theory admits no nonsimple types, then we use Mayer's characterization
of isomorphism for such theories to compute invariants for countable models. If
the theory is small, then the invariant is real-valued, and therefore its
isomorphism relation is smooth. If not, the invariant corresponds to a
countable set of reals, and therefore the isomorphism relation is Borel
equivalent to $F_2$.
  Combining these two results, we conclude that (Mod(T),$\cong$) is either
maximally complicated or maximally uncomplicated (subject to completely general
model-theoretic lower bounds based on the number of types and the number of
countable models).
