well, i'd say the chances to get more and higher tier items is higher at higher difficulties, but that isn't backed with any real data.
Higher difficulty songs give you more XP (although you probably get more per stamina at debut, but i wouldn't be surprised if they change that soon, it doesn't make much sense), more fans and more affection. Fans are useful at the moment because some idols unlock additional communications at 2000 and 10000 fans (there is probably more to come in the future), and at least the 2000 fans commu gives you 25 stars. The affection isn't much of an issue though i think, even though the communications that come with an upgrade give you 25 (normals) or 50 (rare and srare) stars, the limiting factor are the item cards.
But most importantly: debut songs are boring as hell. I mostly play on pro.