Omnidirectional to the horizon? Colinear.
In general, you need length along the axis you want a narrower beam on.
A colinear is long along the vertical direction, so gives a narrow beam, to the horizon. It is horizontally narrow (and rotationally symmetrical), so gives a broad beam in those directions (indeed, a whole torus in the 3D plot).
It's not always exactly the physical cross-section, for example the long-wire and Yagi antennas have directivity parallel to the long axis. There's some hackery between effective aperture and physical geometry, which I don't know much about.
It's more explicit with something like a phased array, where the aperture is literally the array itself, and this effectively defines the resolution of the radiation pattern (as projecting the array's grid onto the radiation sphere), as well as the main lobe to side lobe ratio, or something like that. I forget offhand what angles a phased array can reach, can beams be made in (or nearly to) the plane of the array (for a planar configuration)? The Yagi would seem to suggest it can.
The underlying truth is, directivity in whatever direction is limited by the bounding sphere (or semisphere for ground plane types) versus wavelength: you simply need a bigger antenna for better directivity. But also bandwidth (the limitation is all three factors together, I think?), so a Yagi isn't terribly wide but can be fairly compact, whereas a wideband dish needs to be, well, a whole-ass dish. Or compare Yagi to log periodic, which are similar in directivity, but the log periodic is much wider (longer elements).
Tim