Superman can absolutely beat Hulk
I repeat it like a mantra - Superman is the number one stunnah in DC, Hulk is at MArvel.
Superman can make a strong case (heheh irony) for being as strong as Hulk, if not stronger (up to a certain point) bu t Superman's gig is really winning and saving the day. Hulk is written as a force of destruction > essentially Hulk as he is now is a lovable brute to be pointed in the right direction and left to smash
Superman has all of Hulk's abilities and a whole lot more but his gig is that when the chips are down, he'll be the Joe Montana/John Elway go-to guy to save the day or defeat whatever villains need to be beaten.
On any given day it would be written as a draw. If it came down to it I'd give Superman 6/10 or that one win when it counts
Hulk will get a lot of love in the next few years after Avengers 2 but something tells me Dawn of Justice will be very heavy on the Superman love and power showings (I supect Snyder and crew will be watching Marvel and trying to insert feats that make Superman their number one stunnah)
In a little while I think DC will have its moment in the movies and in the comics and true lore, Superman is the go to for these types of fights