  We study the representation theory of the subregular W-algebra
$\mathcal{W}^k(\mathfrak{so}_{2n+1},f_{sub})$ of type B and the principal
W-superalgebra $\mathcal{W}^\ell(\mathfrak{osp}_{2|2n})$, which are related by
an orthosymplectic analogue of Feigin-Semikhatov duality in type A. We
establish a block-wise equivalence of weight modules over the W-superalgebras
by using the relative semi-infinite cohomology functor and spectral flow
twists, which generalizes the result of Feigin-Semikhatov-Tipunin for the N=2
superconformal algebra. In particular, the correspondence of Wakimoto type free
field representations is obtained. When the level of the subregular W-algebra
is exceptional, we classify the simple modules over the simple quotients
$\mathcal{W}_k(\mathfrak{so}_{2n+1},f_{sub})$ and
$\mathcal{W}_\ell(\mathfrak{osp}_{2|2n})$ and derive the character formulae.
