Mechanical is driven via a driveshaft from the PTO to the winch. Hydraulic is a pump mounted somewhere, usually PTO driven, to a control valve, then you have high pressure hoses running up to the oil motor then is coupled to the winch. Hydraulic is nice because you can mount the thing upside-down on you roof if you wanted and just run the lines to it and you're ready to pull.
Mechanical is driveshaft...and sometimes you have to get a little creative with the driveline for that with pillow blocks and/or chain and sprockets. Mechanical can give you an advantage that you can rev the engine and bump it with the clutch to get a little more oomph out of it...but that's risky as it overstresses ALL parts of the driveline- ...but can get you out in a pinch.
Hydraulic is super convenient, generally easier to use (move handle one way or the other for in and out not fiddle with clutch and shifting pto...) and can be set with a pressure relief so that you don't hurt anything.
Preference is up to the user. I prefer mechanical so I can 'feel' it a little more but I have used and built both.
