It's impossible to not judge someone initially by their words. Many people simply do not agree with me based on how I share my information with others. But we all must do what we can to remain unbaised. Either way.
While Storm and others have fought menacing villans in power levels that are near cosmic to cosmic threats, so has Captain America and the Avengers. Hell, big parts of his story deal with cosmic cubes, things that could destroy entire galaxies. And he's faced people like the Red Skull who wield such weapons. And he, on a large basis, fights people with powers that just make him look like what he was before he even was part of Rebirth. To compare them based on their little villans alone is not the best of examples, as of by now, they've faced villans that go both ways on the scale of power, though Captain on several cases tends to fight these super power levels on his own more than Storm does, only because she tends to appear in a team comic more often than her own, where Cap has his own comic. As for people who can take down a planet? He just went one on one with Titannus, who doesn't require an atmosphere to breathe in, and was far too strong for a team even stronger than the Defenders to take down. Not to mention he's dealt with Galactus, Onslaught (which the X-Men weren't a part of to point out), and a shared experience with the Beyonder. (Though that was more, on all cases, simply surviving encounters with said beings.)
As for Storm actually living in a long term situation where if she walked out the door, she would be shot at continuously? I don't agree. While mutant hating groups have staged attacks before, they don't do it every single day, or wait to find her in public. For the most part, she just seems to go out into public with little, or no problems with the community, where Captain America, for years was in day to day situations where things were lethal to him. Storm, going back, if she were confronted by a group of guys, she could easily defend herself. Hell, if it were a group of Hand ninja's, she could easily defend herself. Captain America is not so fortunate with that one, as he's only a perfect human, and can be defeated by other humans for the most part. Some humans obviously pose zero threat. Put it into context. Wolverine is little to zero threat to Storm, but a HUGE threat to Captain America. He can't simply run away, or fly to get out of danger, making him a harder target, where Storm can, and usually, the act would throw off her assailants. So in the realm of who has done more to survive? I would give to Captain America, since his restraints of powers forces him to have more ingenuity with survival. That, and he was part of SHIELD for a while, and did TONS of espionage stuff, and even was in a huge battle in Latveria. Where, if we were doing single instances, would definitely put him in a good light of experience, since it was him, Logan, Pete, Cage, Fury, and Black Widow up against tons of Latveria's tech and weaponry, where Storm could actually hang out in the upper atmosphere, cause tornado's, rain down lightning, freeze things and such, Cap HAS to be in the trenches, fighting face to face.
So, if we're simply talking who's in a daily battle to keep the human race alive, well, both obviously. Even the Runaways have had their battle to keep the Earth alive. I think the only team that has any large popularity at the moment who hasn't is the Young Avengers. And if you wanted to stretch it a bit, you could say they have by needing to sacrifice a teammate.
Power-wise, Storm has a leg up on Cap. Experience wise, I would say no. But if I'm merely questioning her leadership skills, I really don't have to. She IS a good leader. If she were not, her team would be dead like Speedball's team at least ten times over.