[97TJSport]

Hydraulic: Pulls all day with no real strain.
Cheaper than similarly rated electric.
Doesn't heat up like an electric.
Usually sealed so you don't have to worry about submerging it in water.

Cons: Requires the engine to be running in order to work.
Usually larger than similarly rated Electrics.
Slow line speeds.
Requires replumbing your power steering/upgrading P/S pump in some cases.

Electric: Usually faster than Hydraulic.
Will run even if your engine dies. (at least as long as you have power in the battery)
Smaller than similarly rated Hydraulics.
Cons: More expensive than similarly rated Hydraulics.
Heats up with continuous/heavy pulls and needs to be allowed to cool between pulls.
May require an upgraded battery, as it will kill the stock battery quickly.
Not as forgiving about being submerged in water.

This is not a complete list of the pros/cons of either, just some of the major points.

I chose to go with the Electric, as it will continue winching as long as I have power in the battery. No worries about whether the engine is running or not.

Mike