Several geometries have recently been proposed for spin-transfer oscillators, with the purpose of optimizing the output power and the frequency dependence on the applied current, as well as minimizing the external magnetic field required to stabilize magnetization dynamics. The two structures most compatible with applications involve hybrid multilayers, including magnetic films magnetized in the plane, as well as perpendicular to the plane of the layers - alternatively acting as polarizing layer for the current and as excited layer. Here, we present a quantitative numerical comparison between the two geometries. We find that multilayers with perpendicularly magnetized polarizer and easy-plane anisotropy have considerably better frequency tunability versus current and require lower threshold currents. Nevertheless, steady state dynamics can only be excited from specific, field-dependent initial states, which complicates the design of potential applications. Structures with an in-plane polarizer and perpendicular anisotropy free layer are more reliable, as they are insensitive to the initial state. In exchange, devices based on this geometry require a small (but finite) external magnetic field for operation.