  Extending the definition of $V$-stability conditions, given by Viviani in a
recent preprint, we introduce the notion of \emph{universal stability
conditions}. Building on results by Pagani and Tommasi, we show that fine
compactified universal Jacobians, that is, fine compactified Jacobians over the
moduli spaces of stable pointed curves $\overline{\mathcal{M}}_{g,n}$, are
combinatorially classified by universal stability conditions.
  We use these stability conditions to show the following. The inclusion of
fine compactified universal Jacobians of type $(g,n)$ whose fibres over
geometric points are classical, that is, they are constructed by some numerical
polarisation, into the class of all fine compactified universal Jacobians, is
strict, in general, for any $g\geq 2$. This answers a question of Pagani and
Tommasi.
