gene,
Others have answered with a good description of electric hydraulic brakes (EHB). I'm not sure if that answers your original question.
With elelctric brakes on a boat trailer you would be submerging electrical components. To my knowledge only one mfg produces true electric brakes for the marine environment and they are drum brakes.
With EHB no electrical components are submerged (unless you submerge your trailer past the winch stand). Instead the electric is converted to hydraulic at an electric actuator usually located at the base of the trailer winch stand.
The cost of electric drum brakes will be significantly less than EHB disc brakes. I'm not sure I would recommend true "electric" brakes for the marine environment although I don't have any feedback from anyone who has tried them. Those who have decided to go with EHB disc have provided very positive feedback.
If you decide to go with any type of electric brakes on a boat trailer I would suggest a proportional in-cab electric brake controller such as the Tekonsha Prodigy. The advantages of electric brakes are the ability to control the amount of brake pressure applied on the trailer brakes. For example, in mountainous areas traveling downhill surge brakes will have a tendancy to work all the time and can overheat causing blown grease seals, bearing failure and of course premature wear of the brakes (pads, rotor etc.). Another advantage to electric brakes is there is no mechanical surge actuator and no clunking associated with the movement of the surge actuator. As mentioned above the brakes will also work backing down the ramp (may not be desirable with no boat on the trailer).
Here is a link to a good video that summarizes the differences between timing activated, inertia activated and proportional brake controllers:
http://www.brakecontroller.com/differencevideo.htm
Steve