In the free space, there are no difference from a vertical dipole, i.e. centre feed, a vertical monopole, i.e. feed at one end, and also the old horizontal one, while the length is the same, 1/2 lambda.
Now let suppose we put the antennas 1/2 lambda over PERFECT ground.
Usually that means the feed point for both the horizontal and vertical dipole are
on the same point, crossed, with the vertical extending 1/4 lambda under the horizontal,
but because we're dealing also with a monopole I prefer to put the feed point of
the monopole at 1/2. That should be considered an advantage for verticals in
the next analysis.
While diagrams for the vertical dipole and monopole are still identical, you can't see the monopole's white diagram because it's under the yellow one, there is a BIG difference with the horizontal one.
The horizontal looks a lot worse for DX ! Why ever to build yagis ? Often THAT IS the gain vendors claim ...
But PERFECT ground don't exist. So let we advance for one step. Here the antennas over salt water. If I was Bill Gates I'd have my own little island. Salt water is the nearest one to perfect ground. Look at the two verticals. The pattern is the same, both now with decreasing gain, but still better for dx than the horizontal dipole at 1/2 lambda. Also better than the horizontal at 1 lambda for very low angles.
But now it's the time to come back to ground. An average ground, defined as pastoral, heavy clay soil. But I live in a city. And remember the feed point of the monopole is still 1/2 lambda high... Now the horizontals are definitively better performers. Look at patterns, from perfect ground till average, there are no dramatic change, as verticals do, nor will be for poor ground.
OK. The problem must be the ground. However vendors add radials to verticals. But why verticals have got radials? Now I know I'm entering a mine-field, when my knowledge isn't enough. So, because this file is sooo long and I'm sooo tired, stop for now and we'll try to add four 1/4 lambda radials to the Antron-like monopole the next week-end :-)