Jeffrey Weiss conveys Obama's approach:
He does not claim special expertise or even adherence to the letter of any particular Christian doctrine — saying that his faith is marked by doubt and questions. But he says that his faith is an important tool for him as he makes policy decisions — decisions that nonetheless must also be understood and be justifiable to people of different faiths or no religion.
It's one reason I liked him back in 2007:
This struggle to embrace modernity without abandoning faith falls on one of the fault lines in the modern world. It is arguably the critical fault line, the tectonic rift that is advancing the bloody borders of Islam and the increasingly sectarian boundaries of American politics… Obama, by virtue of generation and accident, bridges this deepening divide. He was brought up in a nonreligious home and converted to Christianity as an adult. But—critically—he is not born-again. His faith—at once real and measured, hot and cool—lives at the center of the American religious experience. It is a modern, intellectual Christianity.
“I didn’t have an epiphany,” he explained to me. “What I really did was to take a set of values and ideals that were first instilled in me from my mother, who was, as I have called her in my book, the last of the secular humanists—you know, belief in kindness and empathy and discipline, responsibility—those kinds of values. And I found in the Church a vessel or a repository for those values and a way to connect those values to a larger community and a belief in God and a belief in redemption and mercy and justice … I guess the point is, it continues to be both a spiritual, but also intellectual, journey for me, this issue of faith.”
Romney's approach is a bit different. In 2008, Romney's campaign internally referred to the candidate's dilemma as TMT (That Mormon Thing):
Romney addressed his religion head on in 2007- through a “60 Minutes” interview and a well-received speech on “Faith in America.” But his reticence was still clear: In the speech, he used the word Mormon only once. Sources say he routinely attends services on the campaign trail- but never in view of the press. Campaign advisers said he has no immediate plans to revisit the issue in a formal way—but sources say it’s never far from internal discussions.
More on whether Romney counts as a Christian here.