Yes its directional, but directional does not mean it will work in only one direction, it means that gain in one direction is maximum. So when car is oriented in the less favourable direction, you will have less gain, but local FM broadcasters broadcast pretty strong, thats why even a single wire will do.
The long antennas which you see on cars(motorized or normal) are variations of J-Pole(Also called north pole) antenna. Thats a omnidirectional antenna, but makes aesthetics suffer.
Rabbit year is similar to a dipole, but the gain reduction in non favorable direction is less. Old TVs has this, and remember you had to turn it to get reception.
The best way to get a omnidirectional FM antenna is to have a turntable antenna. i.e. 2 dipole antennas perpendicular to each other, but that works in a house, but not in a car.
From a purely practical point of view
1. Motorized long antennas are really good
2. Windshied dipole antennas are not good, because manufacturers use just 1 feet long antenna instead of 4-5 feet.
3. DIY dipole antenna will give better performance
4. The shark fin antenna is good for satellite radio(not available in india), but FM reception with or without that will be similar
5. Rear defroster antenna is good as long as defroster is not on.
As for tilting etc., nope, the length should be the same as decided by the equation, it will just effect gain.
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