John – be aware, there is a lot of BS told on Fb, forums and everywhere else by some manufacturers and "power users" and it is heavily misleading the customers. You can read the information you are asking us either from published graphs or from radiation properties files. But there are some "IF"s
A - Graphs
Graphs are good and easy source if i) graphs are true interpretation of the product ii) they are published in usable format (vector) and iii) user is capable of correct interpretation of the graphs. One must understand, graphs are two dimensional representation of three dimensional radiation pattern. You only can tell so little about the antenna radiation properties by using the graphs.. That is obvious limitation of the format.
Patch array antennas have tons of side lobes, but when speaking about radiation properties of patch array antennas, they miraculously "disappear". Everybody – antenna manufacturers in first case - pretend that side lobes are not there (or that they are, if it helps the case, such as null fill). But with this antenna type, side lobes are present all the time. So when you are concerned about where is the patch array antenna radiating @-15 db from max (or bore sight) gain, you have to count with side lobes. I bet that 999 out of 1000 users only consider main radiation lobe, which is of course pretty narrow in elevation beam width. Add the side lobes and everything looks way different.
Example here is the comparison of the elevation patterns of two antennas, KP performance sector for Mimosa and RF elements 30° Symmetrical Horn (both original pdf data sheet attached).
The situation with Symmetrical horn is quite easy to read: at 30° up or 30° down, you are about -15 dB down from bore sight (max) gain. Any degree further, and gain goes steep down hill. The same works for azimuth pattern, as the antenna has circular beam shape (hence the name "Symmetrical")
Now take a look on patch array - one can be easily fooled by an argument that "patch array is only about 7° beam width in elevation", so applying some logical deduction, 30° off bore sight (or 26.5° off that beam width) in elevation pane, either UP or DOWN, one must be god damn safe and the gain must be decreased by a huge portion. Is it? NOT AT ALL. 30° UP OR DOWN from the bore sight on elevation, you still have antenna radiating equal to or stronger than -15 dB from max gain. The reason: side lobes.
Graphs are also easy to cheat with using certain exponential scale that can effectively “mask” the side lobes, etc. Therefor data files may appear as more reliable source - “numbers do not lie” - but again, there are some “IF”s.
B – Antenna files
Now, if you want to use the data that describe the radiation properties: Manufacturers often publish data for certain frequency (often middle of the working band) and let´s say one cut through the 3-D picture. Say this is not the issue if antenna have radiation properties that do not vary with frequency within the working band and are somehow predictable from such a limited information - which exactly is the case of Symmetrical Horns. But it is not the case of the majority of patch array antennas! Just take a look on printed 3-D radiation pattern of typical patch array sector antenna (and that is a not a bad one). They are more complex in real than they appear in graphs or when considering most of antenna files.
What manufacturers and users often ignore on patch arrays and also on other relevant antenna types - if for a reason or not – are again the side lobes. On Symmetrical Horns, side lobes are zero issue, but on other antenna types they are completely opposite. Some manufacturers include the data that describe the main radiation lobe AND also side lobes into antenna radiation files, but some do not! When using antenna files, You should check how exact and true representation of the real radiation pattern those files are. If they are not exact, not complete or manipulated (too good to be true), you are creating model that is not in line with reality, and – what is more important – you are going to make wrong decisions.
As a result in this particular comparison, and just to complete the example case, patch array does not provide you more narrow vertical beam radiation with respect to your goal, despite its main lobe is pretty narrow. 30°Symmetrical horn provides slightly better results for -15 dB beam width, but it also provides way better coverage pattern within given beam width (graphs speak themselves). You can tilt Horn +/- 25°, while I assume KP and other patch array antennas can do maybe half of 25° and only down-tilt. So you even are not able to mitigate effect of those side lobes by tilting the antenna – not only the tilt will not be sufficient, but the resulting coverage pattern will be quite a mess.
The judgement on which antenna is better depends on what job needs to be done, therefor I will not make statements which of the two is better, and it was not the point of this post. (Just in case - ours are the best ). Maybe you are familiar with all things written above and that is good - thanks for reading it till the end. If it was new info for you, I hope it helps.