I would like to add my two cents to this, and break things down a little bit. Batman is a relatable fantasy to because we are cynical. Think about Gotham for a moment, the police are viewed as corrupt or incompetent. Gangs dominate newsfeeds and are trying to destroy Gotham/the World. We have Eco Terrorists and just plain nut jobs obsessed with time, or dates, or fixing things, etc.
Look at the world we live in, people view the police force as corrupt or incompetent, terrorists dominate the news, eco-terrorists get a mention ever so often they pull a bone-headed move, or PETA has a 'good idea', and there are dangerous people out there obsessed with a single aspect of life.
Of course we relate to Batman more, he is what we feel we would need to be, a dark force using the enemies tricks against them. Superman, the big blue boy scout, doesn't. He gets involved with bigger events, because he has the power to be there. Batman is an excellent strategist but a terrible role model.
Seriously, think about the hours of planning, exercise, constant vigilance he needs to stay one step ahead of those with powers. No child would ever get to be a kid.
I am not a fan of Superman, mainly because of his vast array of superpowers, and the Deus Ex Machina of reasons he gets to be so much smarter than everyone else, with crystals of learning or whatever excuse. Crap like that pisses me off, it is just a way to 'balance' things out between Supes and Batman.
And remember, Bruce has a job, apparently. He runs Wayne Enterprises, somehow. But I think this really says something to us as a species though.
Instead of being a nigh-immortal being with a vast array of abilities who fails to bring any significant change to the world, we want to be a very mortal being with severe trust issues who spends more time training and strategizing than trying to improve Gotham by actually making sure Arkham Asylum can hold the crazies, and that the prisons actually do their job. A man with the resources that can actually make sure that Gotham PD has the resources needed to ferret out the corruption within its own ranks and actually stand up against the huge amount of gangs within its heart.
I may not like Superman, but I can tell you this. I could do more to help Gotham as Superman, than Batman ever could as Bruce and Batman.