I'm pretty certain the antennas are omni, and are most likely vertically polarized.
They could be circular, but I rather doubt it.
But to answer your underlying question, it doesn't matter what orientation the antenna is in. If the antenna was directional, and you were pointing it a specific receive antenna whose polarization you were trying to match, polarity would be a concern. But since remote devices can & are installed in all orientations, and signals between hubs and devices may be not be line of sight transmissions....who knows what the polarity is at any given device?
In terms of the Z-Stick, I expect there's a null in the radiation pattern at both ends of the stick, which would arguably be the most important factor for antenna placement. In other words, I wouldn't point the end of the stick directly at another device and expect awesome signal reception!
I've operated mine both flat against a wall in the closet, and flat on a table/shelf in the loft. Neither made a noticeable difference to my mesh (either Z-wave or Zigbee).
My hue hub is presently mounted flat on a wall, and I have no issues whatsoever with the Hue, and I have lights all around the perimiter of my house as well as in the interior.
A better way to improve range is to install repeating devices or dedicated repeaters. The zwave & zigbee networks are mesh networks and expect to have other repeating devices in the network to add range and robustness.
At the end of the day, a home or office environment is a horrible signal environment, multipathing, potential interference, material attenuation, signal blocking, etc are ALL present and quite often significant factors in your home or office. The hub is great, but in that environment, it needs all the help it can get.
S.
