Ultimately, it depends who writes it. There are examples of both dying in eachother's comics, only to have it declared non-canon to preserve the opposing fan base. If you have one kill the other, it brings an end to the tension of what they represent - the real, mortal character versus the invincible ideal.
But really, I don't think either can be killed, for different reasons.
Over the years, Batman has become the most interesting character non-Vertigo DC has to offer, with many books based on him, and it would be financially unwise to ever actually kill him. He's been shot up a million times by people far less skilled than Superman, but he survives anyway, because we want him to. (I've got a comic around here somewhere with Batman being electrocuted to death by some lame villain. In the next issue, Robin shows up, beats the villain, and resuscitates Batman).
Superman on the other hand... well, they have killed him, and it did absolutely no good because he essentially isn't a character. He's a plot device. In the DC universe, in order to immediately define something as evil, undesirable or intolerable, you just have it oppose Superman. He has no flaws, he actually is a living ideal. There are some comics that explore the possibly fascist nature of his authoritative goodness, but these are rare and not aimed at the key demographic - kids. He is, in general, portrayed as one-sided and thus unreal. When he did die (and that comic sold more issues than any other, ever) he was quickly replaced by a multitude of Superman-esque characters, each one as essentially indestructible as an ideal, regardless of whether they were actually killed off in the storyline.
Both have been killed, sometimes by eachother. It never takes.
(EDIT- And a note on "Superman disabling spray" - this has actually shown up multiple times, including in Batman: The Dark Knight Returns. Of course kryptonite is always involved. How did Batman pull it off in DKR? In the words of bat fanbois, which is how they justify all bat-arguments, "he always has a plan.")