Trailer brakes elect v hydraulic
 

Which is better for a small boat (20'). Current rig had rotted hydraulic lines and need to replace with something.

Won't make much difference on a 20' boat as long as you have at least a 1/2 ton truck

If salt water I would go hydraulic disc.

Electric Over Hydraulic is ALWAYS the best choice.

EOH is always a good choice, but it's fairly pricey - especially for a 20' boat. If you want my 2 cents, a surge actuated hydraulic system will work just fine. As for the brakes themselves, disk brakes are much simpler, but require a different actuator with a reverse bypass and Flat 5 (at a minimum) wiring. This might require wiring changes on the tow vehicle. Drums are older technology, but plenty efficient for that size boat if adjusted properly. If you're in salt water, I'd go with disk brakes.

4 different trailer brakes available
1) no brakes
2) electric
3) hydraulic
4) electric over hydraulic

EOH might be the best but not really necessary for a 20ft boat.

Sounds like the trailer has hydraulic surge brakes on it now? If so, that is by far the easiest thing to replace and extremely effective on a smaller boat. Even if you have to replace the master cylinder and the lines, that's not a hard job at all (provided it wasn't an ATTWOOD system, they are out of business, parts are impossible to find). Do you have drum or disc brakes? What sort of lock-out system for backing up does it have? Very basic systems (talking about surge brakes here) will have a locking pin you pull up and out to lock out the master cylinder, essentially. More complex systems (typically using a 7 pin connecter instead of 4 pin) will lock out the brakes whilst backing up via the reverse light signal.
What is the total weight of the towed rig (boat and trailer combined)? If over 2500 pounds I would definitely have some sort of brakes on the trailer.