The advantages, easier to work in your tank during maintenance without removing lights and hood. Also especially easy if you notice a small thing (like a dead leaf or whatever).when walking by. And of course the extra dimension... you can look into your tank from above as well!
Disadvantages - Water loss through evaporation and consequent mineral build up and limescale (negated by large frequent water changes or RO top-ups). Potential livestock suicides. More energy required to heat water.
This obviously sounds like a good idea, in fact people mention lids over open topped a fair bit.I put a 3mm plexi lid on top of both aquariums and the evaporation is almost non existant, no dust going in the water and no more jumpy fish.
I have cats and open top they don't bother with it but they have been used to it sins they where kittensIm assuming if you have cats it's not so good to have an open top tank