Doug,
Speaking generally, satellites are not symmetric, often but not always locked to the Earth's magnetic field lines, and everything from the gain to the circularity depends on "how you look at it." The antenna may be partially blocked, and far off axis a circularly polarized system becomes elliptical, and may even reverse direction.
I have enough RX gain that it is never a problem hearing AO-51, but I do notice there is some variation, particularly WRT polarization. Likewise, I can always uplink on Mode-L, but there is a distinct difference in the power required depending on the direction of the pass.
You mentioned both a beam and a vertical. More details would help to determine whether you are "doing anything wrong," but it sounds as if your gain is low enough that you are hearing the difference a few db makes. The usual questions would be length and quality of coax, pointing accuracy for the beams, use of a low noise preamp, etc.
Alan WA4SCA