I think it would be a safe bet that the beam antenna will hear more than the omnidirectional vertical in particular directions, right? That's the whole purpose of directional antennas. The difference in antenna heights will make some difference at times, but on the whole, that directional antenna will 'do' better.
I don't know what the gain of that m103 is, but it's more than a typical 5/8 wave vertical. The 'catch' to that is that the m103 will have to be pointed in the right direction for you to take advantage of that difference in gain.
'JI' pointed out that it isn't just a matter of the gain, or the take off angle, but the combination of all of an antenna's radiation characteristics. Keeping that in mind, 'Momma Nature' still controls/determines the 'best' height for an antenna to hear a particular signal. Signals almost never always arrive at your antenna at your antenna's 'sweet spot' all of the time. That arrival angle/take off angle changes all the time. To keep that 'sweet spot' -AT- the 'sweet spot' you have to be able to vary the antenna's height along with it's pointed direction. Can you imagine how much trouble that would be? And then 'Momma Nature' isn't very constant, 'she' changes things on a whim, it seems. If cost were no object being able to vary the antenna's height, or having several antennas at varying heights would be nice! (Don't know about you, but I am very doubtful that I could afford that.)
Gain and TOA can be 'worked around', just takes more ability from the operator doing that 'working around'. Things very seldom work out exactly 'right', so when they do, mark it on the wall!!
- 'Doc