A 1/4 wave over a perfect conducting surface (imagine acres and acres of copper sheet) will have a very low takeoff angle and the main lobe will be pretty much right at the horizon. At ground level over average soil with only four radials the main lobe will point up some and you will be several dB down at the horizon. Plus four radials laying on the ground introduces loss and the efficiency goes down noticeably. You now have a ho-hum lo performance vertical antenna.
You need a lot of radials on the ground, enough so the ends are a very small fraction of a wavelength apart to make it closer to a perfect ground, otherwise ground losses creep in. That's all textbook and I've experienced it in the field with various vertical antennas.
Take that same 1/4 wave vertical with four radials and place it 1/2 wave up in the air and the lobes come down a little farther towards the horizon compared to the antenna on the ground. Put it up at 1 wavelength or higher and the lobes will creep down a little more each time you go up in multiples of 1/2 wavelength.
Bottom line to your statement, a 5/8 wave Penetrator with its integral radials anywhere in the air will kick butt on a 1/4 wave whip with four radials laying on the ground. It will have more field strength at the horizon for best local and DX, even at the worst height of 1/4 wavelength above ground and at 1/2 wavelength multiples above ground it will be waaay better.
prcguy
One person touched on it already, but I wanted to also mention it.
A low angle of radiation for a vertical is more dependent on how low to the ground you mount it, not what make and model it is.
A quarter wave vertical on the ground, working off a good radial system, is going to give you a much lower angle, than the most expensive 5/8th's 60' in the air. At 11 meters, a good radial system is as cheap as 4 quarter wave radials laying in the grass.
