David - this again is just not correct. ½ wave antennas, work as 2 quarter wave ones, working together. They do not require a ground plane for their performance. The only real snag is the length - and the need for a matching network at the feed point because it is naturally much higher impedance than a ¼ wave - so usually a coil and capacitor are required to bring it down to 50 Ohm.
Like a ¼ wave and a ½ wave dipole they have ZERO gain. They are often quoted as having 2.15dB gain over an isotropic source - a point source that is purely theoretical - they don’t exist. 2.15dBi and 0dBd are exactly the same. ½ wave antennas have 0dBd gain.
The differences in the designs you mention are due to the vertical angle of propogation. As in where the effective power goes. For a vertical, little goes up, and most goes forward, but the actual angle of ‘maximum launch’ changes. So if you want ground coverage you can choose one design, but if you want the best opportunity for sending it up at an angle, you might pick a different one. Decibels work in strange mathematical ways, but you ALWAYS have to reference them to something else - think of them as a ratio. Manufacturers who use the isotropic source scale look better than another who uses the dipole as a reference. It’s the same argument as comparing a ¼ wave groundplane, or a dipole to a J-Pole or a Slim Jim. The only place more oomph comes from is by changing where the antenna directs it. Antennas just distribute your available power in certain directions.
How about these two explanations Google found for me.
A half-wave (1/2-wave) dipole antenna has a standard gain of 2.15 dBi (decibels over an isotropic radiator) or about 0 dBd (decibels over a reference dipole). [1, 2, 3]
So - confirmation that there is no gain difference between the ½ wave and the dipole.
However - Google also says:
1/2-wave antenna provides roughly 1 dB to 2.1 dB of improvement over a basic 1/4-wave whip
This appears to contradict the other claim - but what it is really saying is that the radiation pattern - that is for the ¼ wave a typical doughnut shaped plot - gets squashed down, making it less sensitive /efficient upwards and a bit better closer to horizontal.
Don’t get excited because 2dB change is hardly noticeable. It’s there, but it’s not a lot.The other upshot of the squash is that they are less good for skip conditions, as the aims is more ground distance. Just remember to check if specs are in dBi or dBd when you need to compare, and unless the specs also detail the vertical radiation pattern, you are just hoping and guessing.
There are lies, big lies and Decibel figures!