That's the thing. For someone with his reputation, Batman's rogues gallery is shockingly weak, and many of them (Joker) get a lot of mileage out of the fact that they know Batman won't actually kill them. Ras Al Ghul and Bane are probably the most capable, with Joker's schtick being that he's "unpredictable."
Cap's typical villains are MUCH worse. Red Skull, Crossbones, Arnim Zola, Baron Zemo, Madame Hydra, and Taskmaster would have a field day, as would AIM and HYDRA as organizations. These are all extremely intelligent global level threats and not broken sociopaths with strange gimmicks i.e. the riddler, mad hatter, victor zasz, etc.
Even spiderman's rogues would give him the fits. Kingpin, Doc Ock, Norman Osborn, various hobgoblins, Venom, Kraven, Mysterio, Tarantula, and Electro would have Gotham in flames in a couple of hours- and spiderman routinely takes on 6 of these at the same time.
Miller's writing aside, Hal Jordan has always been written as extremely underwhelming, given what the ring can actually do. The whole "going evil and turning into parallax" thing was the one time where you FINALLY saw what the ring was really capable of.