Sul is more related to simply being on top of something, to simply be on the surface of something. i personally use it for objects like a key on a table or a pillow on the bed. on the other hand, you say supra when you want to be sure the person you're talking to understands that theres something above something else. in fact, i'd even consider translating supra to above instead on top of, so its more used with things that are alive or very big, like a cat.
I have no problem with the distinctions between the Italian words su and sopra. However, I strongly protest having to translate sopra as "on top of" here. In my part of the English-speaking world at least, we would definitely say the naughty feline is "on the table"! If it were on a shelf or suspended from a light fixture it could possibly be "above" or "over" the table, but that is clearly not the case here.
As prepositions, both over and above can mean "at or to a place that is higher than someone or something," but over is somewhat more common: A light hangs over/above the table. He raised his arms over/above his head. She rents an apartment over/above a bookstore. http://www.learnersdictionary.com/qa/above-and-over. Would DL please accept over as well as on top?
I used "the cat is on the table" which was not accepted. I'm confused--where on the table would the cat be except on the top? Requiring "sopra" suggests that the cat is not only on the table, but perhaps floating just a bit above it. Maybe a Cheshire Cat! Anyway, I did report it (btw, the prompts give "on" as a translation of sopra.)