So this one is kind of easy. Cap is the better hero imo for various reasons but how in the actual **** does he win a single one of his encounters? So maybe he beats Lex. Cool. What happens when Doomsday or Brainiac?
Superman has the ability to lead people, just like CA. He can inspire and be a symbol in Marvel, as he does in DC. Every situation that CA was in, Superman would do the same, if not much better
CA on the other hand, being tossed into DC, he'd either fail or other members would need to carry his load. CA's job would effectively be taken by other JLA members already; most notably, Batman and Cyborg. He'd do a good job of inspiring and being a symbol but too many villains that Superman encounters would kill him
Cap has the best of both batman and superman in regard to leadership and inspiration. Where GENERALLY speaking Batman's there for leadership and Superman is there for inspiration.
What would happen if you brought Captain America's power levels up to par with Superman's? Pure might doesn't somehow negate or elevate a person's stature. You can be as powerful as Superman, and still be a snivelling little c@nt. Look at Ultraman, or Maestro Hulk for example.
But the way Shadow worded it out, it seemed like he could barely think of any Supes villain Cap could beat... whereas there are plenty who either aren't physically formidable or have obvious weaknesses (such as Metallo with his glowing kryptonite heart).