To me, it isn't so much about being "grim" or "dark" - it's how the characters relate to me and how I relate to them. When I look at Clark Kent or Bruce Wayne, I look at people who are braver than me. Who are stronger than me. Who are better versions than I could possibly hope to be. I want to make myself more like them...I don't necessarily want to see myself in them.
I know his ideas on Clark are controversial (American Alien is still sitting on my bedside table unopened), but Max Landis had a little rant after Man of Steel that really helped me understand why Superman is such a fascinating character. The guy has all the powers, and people see that as boring. But, to him, it's not his powers that make him interesting or notso....it's the way he reacts to his powers. That he basically has two options in life - save the world or rule it. And that he decides "why not" try and save it. That, instead of absolute power corrupting him absolutely, absolute power absolved him of all the petty crap that we deal with.
So, yeah, Clark would have problems, but at the end of the day, I think he'd understand how freakin' lucky he is to be who he is. How much fun he'd get to have on a daily basis. He might've lost his whole family, but he's had a great family his whole life. He might be alone, but he doesn't even necessarily identify as Kryptonian.
That's why I liked Smallville's Clark. He has normal human problems (relationships, school, purpose, etc), but at the end of the day, the guy is a beacon that brings a lot of people to the light. At the end of the day, he can run off to Europe with Bart or super-basketball with Pete. My lasting memory of Clark in Smallville isn't him brooding over Lana or wearing the black suit that one season. It's him smiling on the farm. Clark has a great life, and he knows it. Even on the CW.
Even Batman is a similar type. Yeah, he's dark. He's brooding. But even he seems to understand that he has it better than most. That's why he's willing to take punishment to save people - he can and they can't. There's a weird dichotomy between the Batman who is alone and the Batman who keeps rescuing kids and putting them in colorful costumes, but I think it's a natural evolution of the character. Like the boxing gym down the street, some kids need to channel their violence in a healthy way. Bruce knows this as well as anyone.
I don't like the Christopher Reeve Superman, and I don't like the Henry Cavill Superman. To me, they both get it wrong. Superman can't be all happy, but he shouldn't be too challenged either. I don't want to see myself in him. He should be better.