Bionic Saint has the best answer so far.
I'm gonna give it a shot though.
Batman was born from tragedy. He swore to avenge his parents and wanted to make sure that no one else will ever have to go through the trauma that he suffered as a kid. He is Batman all the time. It is the Bruce Wayne persona that he feels is the "mask". He is a self made man, and has honed his body and skills to near peak perfection. He is human and has the cuts, scrapes, bruises, scars and broken back to prove it. He can think on his feet and has a plan for every scenario, and if not, he will make one. Yes he has the ability to take down the entire Justice League if the need should ever arise. We can relate to him, Batman could be me, your neighbor, your friend or even you. It's not out of our grasp to fathom the want or need to avenge a loved one at any cost, even our own.
Superman is the "Last Son of Krypton". Sent to earth to survive a dying world. He was raised be the Kents and taught strict wholesome values. Right and wrong. Balck and white. There is no grey area with Superman. Superman is always Clark Kent, just a small town farm boy. But as Superman he stands for "Truth, Justice and the American Way". To be honest, doesn't that all sound a little dated by today's standards? The guy can do anything he wants and he does. Sure he is a shining beacon that we don't have to kill each other just because we can, but that's about it. How do we relate to an alien? That's why I root for Lex. He may be the bad guy, but he is looking out for the interest of human kind.
As far as the Villains, it's the same as above. Most of Superman's villains are magical imps from other dimensions,robots, other aliens or god forbid a dysfunctional clone.
The thing with Batman's villains is they are human as well. Not only that, Batman as well as us can see that there isn't much separating him from becoming them. He walks the line so we can sleep at night.
I could go on for hours, but this is the short and sweet.