I run both... with top and without... the determining factors to take into account is how far the light is from the water's surface, does the fixture sit on the tank or is it hoisted above via clamp, hanger, etc.? also, types of animals in the tank, will you be likely to have jumping issues? ventilation is something else to consider, if you use other than glass, will it get hot? and what will it do to the rays of light, reflect them? allow them to pass through? Plastic isn't usually a good option in saltwater due to temperature and melting issues. Glass would be the most practical to use as it doesn't block light and it creates a barrier between water and electrical equipment... one of my tanks has a "partial" cover, where only 1 piece of glass sits over the top, just enough to work as a barrier for the light, the rest is open.
Also, don't forget to consider these things:
children putting hands into the tank
dust getting into the tank water
chemicals and other spray cleaners that may be used in the room getting into the water
other pets that may want to go fishing
and salt creep... without a cover, salt creep can be an issue if it's not tended to all the time. I have seen entire walls rot and peel behind a saltwater tank, drywall and plaster both. Woodwork and salt don't mix either.
Lots to consider, but maybe this will help you out.