Waterfall: needs space above; can overflow; matts down after 14 days or so; can attach directly to overflow.
Upflow: needs no space above; can't overflow; does not matt down and can grow much longer; does not use overflow.
This is the answer to "why is a UAS better than a waterfall" not his question which was
What are pros and cons of waterfall vs upflow ATS?
this is a better answer:
Fishbox, I've tried both, upflow and waterfall, as well as a 30 degree slanted single sided. Space constraints in the sump drove these configuration attempts. All worked reasonably well but the upflow was the most difficult to service and requires an air supply to create the vertical bubble flow. Waterfall was most productive but takes valuable space above the sump. Evaluate your space available for your application and configure accordingly.
Here is my pro and con list:
Waterfall (includes a slanted scrubber, and for the most part, a horizontal/raceway scrubber)
At minimum, you need a slot pipe or some other method to deliver water up so that if cascades down the screen, a roughed up piece of plastic canvas (Darice #7 mesh), a pump, and lights (usually on both sides) and a timer (for lights, water flow is 24/7)
Installation has to be above water or tank. Screen can be in sump below the "power off" water level, but lights cannot. So you need to support the slot pipe somehow, and it should be level. Difficult to incorporate into a non-sump system (but not totally impossible)
Since it can easily be 2 sided, you get double the growth area compared to a UAS of the same LxW screen (theoretically).
The water flow requirements usually dictate the use of a pump, because the flow rate is 35 GPH/in of screen width, so rates like 200, 300, 400 GPH actual flow across the screen (after head loss) are typical.
A waterfall scrubber creates a thin layer of high-speed laminar flow that allows nutrients to reach the algae. The laminar flow is what breaks the "boundary layer", which is the term used to describe the area that it microscopically close to the algal cells (flow goes to zero as you get closer to the algae)
A waterfall scrubber can form "streamer" if you don't protect the slot/screen junction. A 'streamer' is my term for when algae grows up toward the slot/screen junction and causes a pressurized point where water can spray sideways, literally horizontally, and get out of your sump. Adding Saran wrap over this area usually does a pretty good job of preventing the streamer, but not the growth. A blackout material does both.
Water can also "creep" along the pipe, adding a piece of airline tubing with a zip tie snaked through it and cinched around the pipe helps to prevent this, as does making sure the pipe is level (or placing it wholly within the footprint of the sump)
Water pressure prevents algae from actually clogging the slot/screen junction. Supplying the screen directly from the overflow will work fine because of this, but anything that goes down the overflow pipe (anemone, snail, etc) can block the flow, so you would need an open-end bypass unless you have a secondary overflow path that can handle the full return pump flow (so that you don't overflow your tank). Dedicated pump eliminates this, as does a return pump tap.
An open-screen scrubber cannot overflow. See above other issues
A closed-box scrubber can overflow, if not constructed correctly and (especially) if not maintained properly. Adding a secondary drain can help prevent an overflow (it will buy you time, essentially). Adding a removable/false bottom to prevent algae growth (and light) from having a direct path to the drain will help prevent the drain from clogging. But it basically comes down to making sure you maintain it or at least check it regularly, as it is not typical for a closed box scrubber to suddenly clog and overflow rapidly (not in my experience). This is because a closed-box scrubber tends to cause water to "build up" inside the box and suspend the algae so that it doesn't detached due to it's own weight, so the thing that would cause an overflow is too much algae growth - and since algae growth is gradual, not sudden, you get the point. As water rises, so does pressure, so a reduced drain flow will self-adjust when the water level above it increases. This of course will only work until the water level reaches the top of the box, but that comes down to monitoring the scrubber and knowing it's typical growth cycle so that you know when to clean it.
An open-screen scrubber can cause salt spray and salt creep on the lights, which may or may not cause issues with lighting, or generally annoying salt creep.
During a power outage, where the lights and pump shut off, an open-screen waterfall scrubber can dry out, but it takes several hours until damage starts taking place - but this depends on the point in the growth cycle, if you have a full screen, maybe 6 hours; a freshly cleaned screen might start to dry out in an hour. A closed-box scrubber will usually last a bit longer.
If a water pump goes out, and the lights stay on, the screen will dry out much faster
A waterfall scrubber can smell a bit during the first few weeks as the initial maturing happens, but this goes away as normal growth kicks in. After that, you would typically only smell the scrubber when you shut off the water flow prior to cleaning. And it doesn't gag you like skimmate smell does
UAS:
At minimum: need a substrate (can be canvas, but this is not ideal for a UAS - crushed quartz bonded to a solid panel has proven to be better), an air pump and air stone/bubbler, and lighting (usually only feasible to light one side)
Since it is usually only feasible to light one side, capacity is reduced when compared to a 2-sided waterfall (reverse of above)
When installed under water line, usually pretty easy to install by just dropping in the tank. This makes it adaptable to just about any tank, and makes it especially useful in biocubes or other sumpless systems.
Requires an air pump to operate, as the bubbles provide turbulence and water movement. The air bubbles are what provides the mechanism to break the boundary layer in a UAS.
Air pumps can be noisy by themselves and can vibrate up against something even if they are quiet, but there are ones that are pretty quiet and high-volume at the same time, so this is more about selection.
The water movement provided by air bubbles alone is much lower than that of a waterfall scrubber. So you get less turnover. If the UAS is a "closed" system (not just a screen strapped to an airstone, dropped in the sump) the constant motion provided by the air bubbles means that the water that is inside the box is recirculated and there is more contact time, so one could make the argument that the water is filtered to a higher level before it leaves the box. In contrast, an "open" UAS might have more inherent turnover by way of normal circulation, with the bubble providing randomness, but the flow might actually carry the bubbles away from the algal mat, defeating the purpose of the bubbles. So this comes down to construction.
Bubbles pop and this can cause salt creep. For an open scrubber, this can be an issue but it can also be remedied in various ways. For a closed scrubber, this can be remedied by placement of the unit such that the bubbles breach the surface within the unit.
On a power outage, the algae stays submerged so it can stay alive for days without too much die-off.
On an air pump failure in a closed UAS, with lights still running, the algae will eventually reach a point of photosaturation as there is no water movement and it will start to turn white and die.
A UAS will generally not smell at all until you take it out of the water to clean it
That's what I can think of at this point.
Generally, a waterfall scrubber has a lot more components and issues to account for related to construction and maintenance, but once you get that down, it's pretty much on autopilot.
The UAS is much simpler to build and more useful for smaller systems where you are not likely to feed a ton. But IMHO they don't scale up well to very large systems.