Why do so many people prefer superheroes with more real-life based powers? They gained their powers from sources that are almost feasible in today's world. I mean, look at Captain America, he's just a guy on very powerful steroids that have no ill side-effects. People love Cap, and it seems to be because he's actually possible in real-life.
Many of the greatest comic-book characters are just normal people. Batman has no superpowers, but he can still take on villains on Superman's level(somehow). Look at Iron Man, he's just a guy in a suit of armor. A powerful, high-tech suit of armor, but it's still a suit of armor. Many others are highly-trained spies and assassins. Even the X-Men, they're people with genetic mutations. Genetic mutations happen in real life, but are usually very serious disabilities. Yet, the X-Men are still slightly reasonable.
Back when comic books first came out, more people probably went along with the stranger, weirder, more unreasonable superheroes because their society was different from ours today. They didn't have the level of technology we have or understood genetics or science as well as we do today. It was easier for such heroes to exist then than it is today because with our level of understanding, we are more prone to ask why?
But I think the other reason people like more realistic superheroes is because we can relate to them. Marvel has always seemed to trump DC in this area, being that it superheroes have to deal real-life problems more often. They deal with taxes, relationships, and other personal issues. They have more clearly defined moral/mental/spiritual weaknesses rather than physical weaknesses. People in today's society like to be able to relate to characters, it helps to understand them better. A character like Hawkeye who fights alongside people like Thor, Iron Man, Captain America, The Vision, etc. deals with being considered a weak link, an oddball(pardon the pun if you get it), and underestimation. These are problems many people in real-life deal with. It's nice to see heroes who fight villains that attack the world deal with issues that we ourselves deal with.