What is the difference between hydraulic and mechanical disc brakes? Are hydraulics more reliable? Or more powerful? All I know (I'm an amateur and a new user) is that hydraulics seem to get more attention and seem to be on professional bikes. I'm just curious, and I probably won't upgrade anytime soon (I currently have cable discs), so I don't need an urgent answer. Thanks!
Hydraulics are used on higher end systems, cables are a certain sign of a cheap brake set, so your observations are correct regarding "professional" bikes.
Cables have the disadvantage of friction that hydraulics virtually eliminate. It is significantly easier to modulate hydraulic brakes, you get more force delivered to the pads, hence more stopping power for the same input, and faster/more reliable and predictable pad retraction when releasing the brakes. As the Hydraulic system is sealed, grit and grim cannot get in to jam up the moving bits, making them virtually maintenance free (replace worn pads is about all need doing) Hydraulic systems are also easier to set up and adjust (with the right tools - next to impossible without them). Cables have to the exact length, and need "tweaking" as they stretch from new.
That said - a good quality and well maintained cable system will out perform a poor quality, cheap hydraulic brake set, so you cannot state "Its hydraulic therefore it's better".
Disadvantages of hydraulics occur when you get a leak such as hole in a hose or blown seal. They are less "field serviceable" than cables, essentially the brake is rendered useless and unrepairable (in the field) by a minor fault - which fortunately happens very rarely, and usually caused by poor transport rather than while out riding.
Watch out in the future for Hydraulic shifters.... Available now if you have the big $$$$, lighter weight than XT and XX level components, almost certainly more reliable and easier to setup....
In addition to @mattnz's response; most cable disk brake systems work by operating one pad only - and squeezing the rotor onto a stationary pad. This means that as the pad wears down, you typically have to wind in the moving pad (usually the outside one) to keep the right bite point.
Hydraulic systems usually have opposing pads that self adjust for central alignment and also as the pads wear out.
(When I manufactured disk brake parts, I used to use cable disk brakes a lot on test rigs because they are so adjustable. However, out on the trail, a good set of hydraulic brakes are much better performing all round)
Here are a couple of downsides of both types, that I have witnessed.
Hydraulic. Leaking oil tends to get into the pads and rotor, rendering the first useless and the second in need of professional cleaning.
Mechanical. Cable failure is very perilous. Essentially one moment you have full stopping power, the next moment the brake is disengaged fully. Additionally, this tends to happen when you squeeze the brake lever hard. When does one squeeze the brake lever hard? Correct - when you need to stop NOW and HARD.
The first incident I only observed. The second has happened to me multiple times with possibly misconfigured Shimano BR-M416