1/2 wave is quite similar to the quarter wave antenna where its main advantage is it doesn't require a ground plane to work as designed. There are versions that provide a bit of gain, but those also are somewhat directional (directionality increases with gain).
5/8 wave antennas generally gives about 3 dB of gain, is longer than the others and requires a loading coil to work correctly. It's omnidirectional, but has a high angle wave (so it works well when the site is not nearby and on a tall tower or mountain top, but not so well when the site is nearby and on top of a tall building). It requires a ground plane to work as designed.
Hope the Above information has given you new members a idea how different antennas work & hope the above information has helped you out.
& here is a image how different antenna`s work,
