  We perform a detailed comparison of results of the Gamow Shell Model (GSM)
and the Gaussian Expansion Method (GEM) supplemented by the complex scaling
(CS) method for the same translationally-invariant cluster-orbital shell model
(COSM) Hamiltonian. As a benchmark test, we calculate the ground state $0^{+}$
and the first excited state $2^{+}$ of mirror nuclei $^{6}$He and $^{6}$Be in
the model space consisting of two valence nucleons in $p$-shell outside of a
$^{4}$He core. We find a good overall agreement of results obtained in these
two different approaches, also for many-body resonances.
