Let me be blunt, I don't like either of these two candidates. If Gingrich or Romney is the answer, it is a pretty damned stupid question. Unfortunately, one of these two is probably the answer to the question: Who will run against Obama with more than a single digit percentage chance of victory?
My gut would love to beat them with sticks, but Christian charity obliges otherwise, and to at least make an attempt at being fair to them. So here is my praise, faint as it might be:
Is a husband of one wife and seems to have raised functional children. Maintained his financial privacy as long as was feasible, but is now shown by his tax returns to be very generous (around 15% average, which is still way above average even if one neglects his expected Mormon tithe). That he never trumpeted his generosity speaks well of him. Romney also apparently possesses considerably more than the average level of self-control (I'd say 2 sigmas, maybe more). Newt might even have ordinary (+0 sigma) levels of that same quality. Let me explain:
Romney, and especially Gingrich are both very high status males. Most of us have to work to some degree to make attraction to the opposite sex happen. Some of us have experience with unsolicited indications of interest from them---as I did, for instance, when my status was enhanced by being a ranking representative in the student governing body at a large university. But I'm willing to bet very few of us have any experience at all resisting a deliberate onslaught of temptation in the manner that a Romney or a Gingrich receives as a matter of course. It is for this reason that I occasionally find a slot for Tim Tebow in my prayer list, and hold him in great esteem for his manifestly superior self-control, which we Christians deem one of the 'fruits of the Spirit'.
Indeed, Christianity has always recognized this, even back on the Sermon on the Mount prior to the Resurrection. Simply because you may not be attractive or have no 'game' in no way immunizes you to the spiritual sin of adultery. God looks to the condition of your heart and not your capability to find willing partners for sinful purposes. Many are perplexed by why God loved King David so much, despite his appalling behavior in the Bathsheba/Uriah affair. My intuition is that most of us, faced with the same intensity of temptation and in possession of the power to paper over the difficulties that King David had, would fall just the same as he did. For this reason I'm inclined to be less harsh in my appraisal of the character of politicians who commit adultery than I would otherwise be inclined to be. I'm also, in the spirit of 'avoiding the occasion of sin', seriously disinclined to run for any significant office.
And Newt, I did promise to say at least a few things positive about him. Newt, in conjunction with his brother in spirit, Bill Clinton, did accomplish significant welfare reform back in the 90s. They also accomplished something a lot less ruinous in terms of living beyond our means than did Bush II and God forbid, Obama. Finally, in Newt's favor, he is one of the only prominent governmental figures who vaguely gets the notion of civil defense (check his forward to One Second After). The condition of our civil defense apparatus and the brittleness of our infrastructure (especially the power grid and the Just in Time system) is appalling, and could easily turn survivable setbacks into outright catastrophes. Newt, given the proper position, might actually move towards doing something about this problem, if he can keep his attention focused long enough.