You've hinted at the difference - beamwidth and directivity. As you increase gain the beamwidth narrows. In the case of a vertical antenna like that means you want to see the main lobe(s) of energy flatten towards the horizon.
This is a very simple simulation run comparing a generic 1/2λ (dashed black reference trace) whip to a stacked 5/8λ collinear whip with a 3/8λ stub coupling (solid red line).
It was run in freespace (e.g. no ground) and with perfect length elements. IOW, don't read too much into this as an example of real world characteristics or actual gain you should expect, just trying to put a visual to what I'm saying. Oh, also, the pattern isn't perfectly symmetrical due to the models I built and the way the antenna simulation tool works (it's called NEC).
But beamwidth is defined as the region bounded between the points where the radiated power falls 3 dB below the peak point. So I've put the blue (on the collinear) and green (on the 1/2λ) bars showing those approximate points.
Since the chart uses 0 dB as the outer ring the blue region should be roughly where the red trace intersects the -3 dB ring. Likewise the peak point on the reference is around -2 dB so the green bars indicate the point where the dashed line intersects with the -5 dB ring.
So the 110° beamwidth compared to 28° I hope makes sense, that being the angle between the pairs of bars, very roughly. In theory. You know, sort of.
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Now the questions are (1) what about real world performance and (b) does it make any difference. That's kind of a contextual answer. When you put each of these antennas on your truck they are not going to look like the ideal patterns.
Simply changing the run from free space to putting the antennas over average ground changes things (these are very simple models so the patterns I get don't necessarily match exactly what might be published in references or marketing material). The dashed is still the 1/2λ and solid red collinear. Beamwidth measurement is changed obviously due to the ground plane. You get a gain improvement, though.
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On your truck this is probably a pretty fair indication of what you can expect I'd think. But consider that UHF is primarily line of sight. Even with 5 watts and a 1/4λ on your roof it's entirely possible in clear topology you'd be limited by the curve of the Earth and not enough antenna height more than signal strength.
The problem comes down to what's blocking you. With landscape and buildings increasing signal strength isn't going to really help. Rock and steel are outstanding at absorbing and reflecting energy. So if 5 watts doesn't do it 50 or 500 is only going to heat the rock more and create additional multipath issues. Getting a clear view is your solution.
Now with vegetation it's a little different. Leaves and brush absorb RF energy but not as well as rocks. Think of it like holding up a granite tile verses a cotton shirt to a light bulb. The granite is completely opaque while fabric isn't. So focusing more RF energy on the horizon in trees might help.
But also look at the patterns and think about your aspects to other stations. To get that extra couple of dB in absolute peak gain you really do concentrate your energy. If a station is maybe even just 15° higher than the middle of the main lobe you lose around 8dB of gain and at 45° it's down 20 dB, completely deaf. And I doubt the lobe at 90° is of much help. The 1/2λ is obviously more forgiving.
And think about being mobile you antenna may not be particularly rigid and the aspect is constantly changing as it flops around in the wind. That means you might hear the radio constantly going from S9+ full quiet so barely audible static (this is called signal fade). That's why you see high gain antennas like collinears built into rigid fiberglass or plastic tubes (called radomes) so they are always vertical.
FWIW, I also ran a 1/2λ (reference dashed) compared to a 1/4λ (solid red) using the same characteristics for feedpoint and ground as in the second graph just to give a feel for how gain and coverage are interconnected. There's 2 dB of difference in absolute gain just there. So from a 1/4λ to a collinear is around 4 to 5 dB of difference, which is certainly significant. That's equivalent to roughly 2.5 to 3 times more transmitter power.
There's trade-offs to deciding on which criteria to prioritize, it's not a simple decision. A lot of people, hams anyway, keep two antennas in their truck. A low gain one that's low profile so it doesn't hit overhangs and doesn't fade in-and-out. And a high gain in case you need it.
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