Surge brakes are hydraulic and thus there are the maintenance issues of fluid, pistons etc. In order to back up (especially up hill) you have to mechanically lock out the braking system so the brakes are not applied as you back up. (There are also electrically activated lock outs available for surge brakes). Advantage - no controllers necessary on tow vehicle and braking action is proprotional to how hard you stop the tow vehicle.
Electric brakes are simpler to maintain. and are less expensive, especially if you want to have brakes on multiple axles. But the tow vehicle has to have a brake controller (with a wire run back to the trailer wiring connector.) A good controller will cost about $100 is simple to install. Most electric controllers these days are of the time delay type and 'ramp up' to full current to the brakes over a short period of time. That way the brakes on the trailer are not just ON or OFF but a gradual application of trailer brakes. Usually, controllers also have a maual button for separate activation of the trailer brakes without applying the tow vehicle brakes so that if you are going down hill and the trailer starts getting a little squirrely (i.e. the trailer is pushing the tow vehicle), you can apply the trailer brakes to calm things down.
Obviously, electic trailer brakes are not a good idea for boat trailers that are frequently submersed in water. They do alright in normal road spray condiitons.
With respect to brakaway systems, the surge type already has a built in sytems for brealkaway situations - a pin is pulled and the brakes are applied. The electric type need a separate breakaway switch and a trailer mounted battery to energized the brakes (however, I just connect the switch to the battery of my power washer unit).
Rental yards use surge sytems on their trailers because of the variety of tow vehicles and all 'control' for having a proper braking system is in their hands.
The electric systems offer a little bit more contol over the braking action on the trailer.
Got more questions on trailers and brakes? Just ASK.