I'll assume we're talking about DISC brakes.

The advantage to hydraulics is that they self-adjust (so long as you center them correctly). Mechanicals have to be hand adjusted and re-adjusted periodically in response to pad wear. For DH riders this is a particular concern as they may need to be re-adjusted in the middle of a run which isn't easily accomplished at speeds exceeding 30mph ;-)

There is ZERO difference in terms of mechanical leverage. Each system will have it's own leverage ratio. On mechanicals, this can be tuned with levers like the Avid SD-7. I'm not aware of any hydraulic system that allows you to adjust the system leverage (only the pad clearance).

This post will be followed by people who do not understand mechanical leverage claiming that hydraulics have "more power" because hydraulic mechanisms more apt at expressing leverage given the size of the components. They completely forget that the amount of leverage you can express is limited by the travel in the hand lever. Increasing the mechanical leverage increases the travel in the lever and you only have so much of that before the hand lever hits your knuckles or the bar.

Mechanical Disc Brakes are more then capable of expressing the same leverage as a hydraulic systems. If you don't believe cables disc brakes are "powerful enough", try hooking them up to cantilever levers and see what happens ;-)