What is the difference between hydraulic and mechanical disc brakes? Are hydraulics more reliable? Or more powerful? I'm curious since, hydraulics seem to get more attention and seem to be on professional bikes.
Hydraulics are used on higher end systems, cables are often a sign of a cheap brake set, so your observations are correct regarding "professional" bikes. However there are very good cable disc brakes (e.g. Avid BB7's) that are the exception that proves the rule. .
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 grime 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.
Another reported problem with hydraulics is boiling of fluid. This is more of a problem on road bikes where mountain descents of 100's of vertical meters in a very short time are more common. With overheated fluid initially the pressure in the system stops the fluid boiling. When the brake is released (even for a moment), the pressure comes off and fluid boils, and the brakes no longer work - at all - the lever just goes all the way in. Another thing that can happen is the rider stops with no problems, but the heat in the calliper (no longer being cooled by airflow) migrates to the fluid over the next few minutes, so when the rider rides off there are no brakes. (This is different to disc fade where the pads and disc overheat and brakes loss effectiveness slowly - both types suffer this equally.)
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.... (Update 2015- Electric shifters mean these will not become main stream.)
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
I will give you this:
As is true with everything, there might one or two exceptions on top-end models (usually fashion top-end, not performance top-end, i.e., the bike brands that you see on podiums ALL run hydraulic disc brakes) where there will be cable-actuated disc brakes, but what more convincing can I do when I tell you that everybody concerned with performance runs hydraulics?
It is also true hydraulic disc brakes have their specific problems - such as the fluid boiling, but these are solved in most modern iterations of hydraulics, road or mountain. Modern hydraulic disc brakes are reliable, easy to modulate and extremely powerful. Even the cheapest models, for example.
Of course you will hear all sorts of people saying how their disc brakes gave them problems, but this is true for everything. Suspensions, wheels, frames (cars, the latest Ferrari 458 and Porsche GT3 both had a problem where they catch fire, and they are extremely high-end products. Sometimes these things just happen and a bad series leaves the fabric). Cannodale, a really good brand, has a recall because a fork could potentially break, which is extremely dangerous. Is cannondale a bad brand? No, this just happens sometimes.
There are disadvantages of course, mainly that maintenance is potentially more costly as you will need to bleed them every once (a year? I do it every two, never had problems) in a while (my shop charges $60), but hydraulics are totally worth it: they are more powerful and easier to modulate. For example, you can brake with one finger - they are that easy to modulate and that powerful, while you keep most of your hand holding the handlebar, having a better overall control. Do this with mechanics..
But despite this big discussion, the best think you can do is go to a shop and try both: I am sure you will be convinced.