  Let $k$ be a field with a real embedding. We compare the motivic slice
filtration of a motivic spectrum over $Spec(k)$ with the $C_2$-equivariant
slice filtration of its equivariant Betti realization, giving conditions under
which realization induces an equivalence between the associated slice towers.
In particular, we show that, up to reindexing, the towers agree for all spectra
obtained from localized quotients of $MGL$ and $MR$, and for motivic Landweber
exact spectra and their realizations. As a consequence, we deduce that
equivariant spectra obtained from localized quotients of $MR$ are even in the
sense of Hill--Meier, and give a computation of the slice spectral sequence
converging to $\pi_{*,*}BP\langle n \rangle/2$ for $1 \le n \le \infty$.
