Either hydraulic or electric will generally do an adequate job, but either one has to be properly installed and supported to perform at an optimum. The best electric winch won't work well or for very long if it has only a 60 amp alternator and a single battery to support it. A hydraulic winch won't make enough power to pull a toy wagon if it does not have sufficient volume and pressure supplied from the pump.
Hydraulic only works when the engine is running, electric will work with the engine off, although not for long. There may be a time when all you need is 60 seconds of power to get out of trouble, but the engine won't start (deep water crossing and a drowned engine.) Here, an electric winch could get you out of the water where you could then deal with the engine problem. If you don't do deep water, it might not be an issue. This is also true of pto winches. I knew one vehicle with a tremendous pto winch driven by a 4 cylinder turbo diesel. The winch was so fast, it was unbelievable. The guy tipped his Cruiser over in shallow water, putting the intake snorkel under water. Even though the diesel would have run lying on its side, it couldn't because of the intake under water. He had to get someone else to pull him back on his wheels before he could start the engine. If he had been without help, he would have been in big trouble.
Most of the hydraulic winches I have seen which were not effective were running on a power steering pump along with the steering gear. A p/s pump will usually make sufficient pressure, but will not produce any volume, and without both, a 12,000 pound winch makes about 2,000 pounds of pull, and is so glacially slow as to defy description. All that happens is the fluid gets hot from being overworked. That, and everyone else in the group gets hot from having to stand and wait while the hydraulic guy dithers away the daylight.
On the other hand, I have seen hydraulic winches with industrial pumps dedicated to running just the winch, and these winches pulled so hard and fast that you had to get out of the way. The only winch I have seen run faster was a PTO winch.
So, if you want a hydraulic, I would suggest finding a good industrial pump rated to the pressure and volume needs of the winch so that it can perform at rated capacity. find a means of running the pump as an accessory on your engine. If you can run it through an electric clutch, like an a/c pump, even better.
Electric winches need proper power as well. I have operated the same 8274-50 for 6 years. Running on a 60 amp alternator and a single battery, I would quickly run voltage down to around 10 volts, say in 30 seconds or so. Even fried a CD player that I forgot to turn off while winching when the voltage dropped below 10 volts. Permanently DOA. With a 140 amp alternator and a single battery, I got another 30 seconds before everyting shut down. Stereo number two hit the dumpster.
Same winch on a 210 amp alternator and dual Optimas will pull all day long without a serious drop in performance. Longest series of pulls was a quarter mile up a 100% slope in about 35 minutes, with the only recharge times while the anchor point was being reset. This was during the 2002 Outback Challenge in Oz. Its hard to beat an 8274 when it is running right.
So, with proper support, either style of winch will do the job. Without proper support, neither will be satisfactory.