Can someone please explain to me what technology can be more finely controlled, and the how and why it is that way? And link scientific articles if possible? I'm having trouble finding any and would like to expand my knowledge on the subject.

On its root it is a basic geometry: The theoretical angular precission in radians is the ratio between focal length (optical distance between the light source and the optical element) vs the size of the light source.
On top of that you have errors caused by the alignment and optical element shape precission. Assume that could be kept under control by the quality of the manufacturing/installation work.

So the smaller the light source and further away the beam shaping element is designed to be from it, the better the precission.
The optics size is limited by the assembly size and weight restriction, here the lightweight halogen (needs no explicit cooling) allows more weight budget to be allocated to the optics. But once the optics is the dominant part (way heavier than e.g. LED heat management components), you are at the limit here.
The light source size by how much light it needs to generate, so in other words its surface brightness.
Here I think the LEDs are offering better values, so allow the light source of a given flux to be shrunk to smaller size, so allowing smaller optics for the same beam precission. Or in case of incandescents (even halogens), you need to go to higher filament temperatures (photo lamps). But I guess the halogens are losing to LEDs here also., so my guess is, for the given assembly size, the smaller LEDs may allow higher ratio, so more precission beam control.

Other aspect is the optical efficiency: How big percentage of the total optical output you may redirect into your precission beam. For a classic light omnidirectional source like halogen or so, that means redirecting the light from all directions. And that is mathematically impossible task, so you will get stuck with geometrical (efficiency assuming no light loss passing lens material, nor reflecting from a mirror) efficiencies in the 50% or so when forming a single narrow focused beam line. And already that means the fixture size to be more than 2..3x the focal length, in each direction.
Leds with their inherent beam pattern to be already only in a half sphere have already an advantage of their mount and conection not obstructing the light. So geometrical efficiencies in the 70..80% are not that unattainable.

If you combine it with the shorter focal length, for the given overall assembly size limits, with LEDs you may attain better efficiency, so suffice lower total flux output light source, allowing it to be smaller so give better precission.
But in real life there are other factors.
 On higher power application you may still loose on the weight required for the heat sinking.

And there is also other aspect, the one that is the most volatile: The cost of the LED vs the halogen. The halogen lamp itself may be cheaper, but has very limitd life, so the assembly must allow its easy user replacement (LED can be rasonably designed to last the system lifetime, halogens mostly can not). That cost extra money and mainly for low power makes the halogen systems more expensive to make than the LED. Either way, the cheaper the light source, the more money budget remains to spend on the optics, allowing you to get a better quality one, so it could be also a factor in the "which offers better beam precission", if the total budget for both is equal.
Generally for short byrn time (when the energy cost is not an issue), higher power levels favor the halogens, lower the LEDs. If the energy cost is an issue (e.g. when the higher power asks for more expensive batteries to have the same runtime, or heftier power installation to feed it, or just plain cost of the energy), LEDs are the cheaper way, so allow budget for better quality optics.

And to add a bit more mess, many applications are governed by regulatory restrictions, which do not allow you to fully utilize some technology, so bring the other one back to lay (like car headlight front lens brightness needs to be within a limit so imposing larger lens for the given output, otherwise you need extra system for keeping the headlights clean during driving, which means other expenses and complication), or a side effect of one technology provides another necessary function, which you would need to manage by a separate system with the other technology, like heat radiated from halogen keeps the front headlight lens dry so optically clear even when e.g. wet.

Due to LED's not being able to emit as much light in a small surface area, wouldn't that effect how well they can be focused? Like say I wanted a beam that was 20000 lumens focused into a tight beam at 100 or more feet away, Wouldn't that be a bit harder to accomplish with an LED than a HID (for example) due to heat sinking issues and the fact that no single diode can emit 20000 lumens?

I imagine it is possible to achieve a tight beam by precisely aiming each individual LED reflector... But couldn't a halogen be focused more tightly due to it's smaller, singular Tungsten filament?

It is indeed the question of the tungsten filament vs LED chip surface brightness.
The LED brightness went very steeply up with modern versions, so far I would guess it became higher than the tungsten filament.

It also depends on how hard you want to drive the LED, i.e. how much lifetime you need from it. If we are talking about short flashes, then I guess you may get better with LED's (as few 100's hour of cummulative full power operation time would still give many years of service). This could be relevant for some portable lantern, where you can not afford the high power for longer time because of the limited energy available in the batteries.
For long time operation it is question, what will yield better, but I think using LEDs in the format of an array of lower power reflectors each using smaller chip (so it still yields desired beam angle) has the chance to yield better performance for the given size. More over the "array way" will yield rather flat assembly (the depth will correspond to the focal length of the individual reflector, regardless of how many of them are used in the array), so when compared to the overall volume, it will allow bigger cross section so even longer focal length vs the individual die size. So could lead better result even if the brightness is the same, or offset the eventual lower brightness if such hard driving is not acceptable.

But then we are talking about something requiring precission plastic molding, things out of the reach for DIY (for the small size reflectors the tolerances and the ability to process batch of 100 pieces would be out of reach for home fabrication).

I would lean towards LED for the higher precision of alignment between the source and the beam forming elements as the LED is affixed to the structure HID / incandescent the source is suspended in a pressure vessel and likely a separate lamp structure from the beam forming elements
would imagine the * best * source would be those sodium microwave lamps assuming a very highly controlled design with MASSIVE cooling (liquid filled elements)

Another advantage of LED is its modularity.  Although the surface luminance of each chip can be extremely high, the total luminous flux is low and that limits the luminous intensity of the beam.  However, you can then add a second LED, lens and heatsink, or a tenth or a hundredth and build up large arrays,  the resulting assembly might be very large but the optical prevision of each is outstanding.  The net result is far better than possible with any other light source.  Even the intense brightness of the UHP mercury arc for projectors has given way to solid state alternatives.

In every example I came across in recent years, the optical performance of LED systems vastly exceeds that of any other light source.