Manufacturers specifications vary greatly.
Some are inaccurate, others use different measuring methods using different values.
You are also comparing three entirely different antennas in the examples shown. (Eg: comparing apples with oranges)
Gain is not the only factor which determines performance.
Location in relation to distance between the receiver and transmitter, the polarisation of the signal, terrain, etc, all play a part.
Eg: If you are in a strong signal area, an indoor antenna will likely be just as effective as an outdoor type.
Yes, a directional antenna such as the Hills yagi will have more gain due to it's narrower beamwidth and directional design.
It also has a single polarity, horizontal or vertical, depending how it's mounted and will be better-suited to receiving signals over a greater distance than the other antennas, providing all transmitters are located in the same direction and all signals are of the same polarisation.
The Fracarro antenna shown is designed to receive both horizontal and vertical signals and is largely omnidirectional.
It will have less gain that a yagi type, but is more versatile in that it can receive from all directions and signal polarisations, is physically smaller, stronger and less likely to be used by birds as a perch and looks less obtrusive.
The third 'horizontal ring' example is omnidirectional, but designed primarily to be mounted for horizontal polarisation.
I have personally installed the Hills and Fracarro antennas, but have no physical experience with the ring-type.
It's important to consider what radio stations you may want to receive.
High-power commercial and ABC FM stations transmit mixed polarisation signals, so that either vertical or horizontal antennas can be used.
Low-power and community stations mostly transmit vertically polarised signals.
Where signals are a single polarity, your receiving antenna must match that polarisation because using an antenna that is the opposite polarisation (Eg: 90 deg out) will drastically attenuate the signal and for a low-power station, that may make it unable to be received.
You show your location as Canberra.... if all your FM signals are coming from Black Mountain, (and of the same polarisation) any of the antennas shown will work well. Even an indoor antenna will probably be sufficient.
It all comes down to what stations you want to receive, how powerful are the signals, their polarisation, terrain and local interference levels, etc.
Basically, the same principles of selecting a TV antenna apply.
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