I would agree with Waldo, jake has asked an excellent question... a few observations about what would be different:
Firstly, continued slavery, most likely on a greatly increased scale. Your own Wilber Wilberforce was driven by his Christian ideals to eradicate slavery in England., while it was defended by powerful politicians on the basis of economic need. Slavery's eradication in the U.S. was the result of dedicated churches and Christians who were counterparts to Wilberforce.
There would have been 500,000 fewer violent, battle induced deaths between the years of 1861 and 1865 here in the U.S. since there would have been no Civil War to free men based almost entirely on Biblical principals.
Science probably would not have advanced so far so quickly except for the likes of Nicholas Copernicus, Sir Francis Bacon, Johannes Kepler, Galileo Galilei, Isaac Newton, Max Planck, and even Einstein who said "Science without religion is lame, religion without science is blind." and inumerable other early scholars and scientists whose inquiry was based on reconciling their Biblical views and observation of the natural world.
There would be many more sick and dying people in their relatives homes, since the Christian based hospitals who support care to any and all who walk through the doors wouldn't exist.
Crimes would be more numerous, but wouldn't be viewed as crimes. By that I mean, in a totally natural world, why wouldn't the paradigm be "survival of the fittest"? What would be wrong with the strongest, meanest human dominating others... wouldn't that just be natural? After all, it's Dawkins who says nature is "red of fang and claw"... In the interest (believe it or not) of brevity, I'll only offer these examples, but many more abound...