I always love the tired old "he's powerful so he's not relatable" argument.
Powers aside, Superman's got a lot more in common with the average joe than Batman. He grew up in a middle-of-nowhere town, and never fit in anywhere he went, which grew even more complicated when he discovers his real origins. He tries to be like everyone else, but his powers and the job that comes with it means he can never do that. Even surrounded by other superheroes, he's always put on a pedestal above the others, so he can never be just 'one of the guys.' And his upbringing on Earth means he's not at home with other Kryptonians, either. So no matter how much good in the world Superman does, no matter how many friends or loved ones he has, on that one basic level of having a shared experience with others, he is always completely alone.
That basic need to try and reach out to his fellow man, even though he can never really fit in, that struggle to establish his own identity, is one of the key elements of a heroic-everyman character. The fact that he's got incredible superpowers just means his conflicts are on a bigger scale, with the stakes that much higher if he fails. He's got plenty of tragic elements to his character, but he doesn't let them define him and turn into a 24/7 brooding-angst-machine like Batman. To me, that makes him a lot deeper than the guys who just shout out their drama at every given chance.
Contrast Clark's upbringing with Bruce, who spent his childhood spoiled rotten in one of the richest families in the world, then ran off for years on a quest that none of us could ever have enough money to afford. He then got to come back and take over a billion-dollar corporation that he had no hand in creating, and use his family's and his company's fortunes to make a bunch of weapons and gadgets that make him unbeatable. He never loses a major fight (especially not if he has "prep time") and always gets to be the guy who's right when the heroes start arguing. In that sense, he's far more invulnerable, and thus a more shallow character, than Superman ever was.