  Using time-dependent density matrix renormalization group calculations we
study the transport properties ($I-V$ curves and shot noise) of the interacting
resonant level model (IRLM) in a large range of the interaction parameter $U$,
in the scaling limit. We find that these properties can be described remarkably
well by those of the Boundary sine-Gordon model (BSG), which are known
analytically (Fendley, Ludwig and Saleur, 1995). We argue that the two models
are nevertheless in different universality classes out of equilibrium: this
requires a delicate discussion of their infra-red (IR) properties ({\it i.e.}
at low voltage), where we prove in particular that the effective tunneling
charge is $e$ in the infra-red regime of the IRLM (except at the self-dual
point where it jumps to $2e$), while it is known to be a continuously varying
function of $U$ in the BSG. This behavior is confirmed by careful analysis of
the numerical data in the IR. The remarkable agreement of the transport
properties, especially in the crossover region, remains however unexplained.
