Hydraulic winches are more robust in that they can winch all day without overheating. If your Jeep's engine is stalled this type of winch typically cannot be used. MileMarker is the leading manufacturer of these. They are most commonly connected to the power steering system, which must be beefed up in many cases. PS coolers are often added to this setup.
Warn, Ramsey and others make electric winches which are more convenient if you do not plan to be your club's winchmaster.
Runs all day without overheating, less susceptable to water/elements, runs off "tap" into powersteering which requires that the motor be running and can cause premature wear to system.
Electric:
Faster, runs when engine is off, satifactory for most jeepers, more susceptable to water/elements, prefered/more common so parts are easier to come by.