In strong-field ionization (SFI) of polyatomic molecules, the participation of multiple electronic ionization channels is emerging as a key aspect. In the molecular frame, each channel is expected to show a characteristic dependence of the SFI yield on the polarization direction of the ionizing field. We apply a new angle- and channel-resolved SFI technique to the polyatomic molecule 1,3-butadiene and compare these molecular-frame measurements with two leading theoretical models.