First, it's absolutely necessary to make clear what we're comparing. If you want to compare our historical sources about Jesus vs. our historical sources about Joseph Smith, Mormonism wins hands down. It is arguably a Phyrric victory, though, because much of what we know about Joseph Smith is rather embarrassing (and makes you wonder what we'd know about Jesus if the historical record were better).
If you compare evidence for miracle claims, the case is more equal. Given that even many fairly conservative scholars deny gospels were written by eyewitnesses, the only thing eyewitness evidence we have for any major Christian miracle is Paul's testimony about his own vision of Jesus. On the side of Mormonism, we have a statement signed by three people attesting to their vision of the angel Moroni, which is supposed to authenticate the book of the Mormon. Mormonism does better here, if only by a little.
What Reppert wants to compare is the general historicity of the New Testament vs. Book of the Mormon. From an historical point of view, the Book of the Mormon is certainly nonsense. Why it is so edifying for Christians to have a semi-reliable record of mundane historical events is beyond me though.
Furthermore, the contest is again more equal when we compare the Book of the Mormon to many events of the Old Testament. Genesis is historically nonsense, and just as much contradicted by scientific evidence as the Book of the Mormon. It is not clear whether the exodus story is complete nonsense, but an event on the scale that the Bible claims would have left archaeological evidence that we simply don't find. The Book of Daniel bears a striking similarity to the Book of the Mormon in that its ending indicates that it was "found" long after it was allegedly written, though Daniel seems to have drawn more on actual events than the Book of the Mormon.
In general, I think claim of Christian apologists that Christianity has better historical evidence on its side than any other religion works only by ignoring modern religions like Mormonism, Spiritualism and UFO cults. As noted above, though, the information we have on modern religions tends to be embarrassing to those religions, but this should only make us suspicious of the less well documented religions. Yet that's a post for another day...
UPDATE: Here's an e-mail I found in my inbox today. I post it for the benifit of Christians who are so ready to swallow the claims of Christian apologists:
You suggested that Mormons have a slight advantage over the Bible because they
have 3 eyewitnesses versus only one for Jesus. If you grant that the gospel
authors and the author of Peter's epistles were eyewitnesses, the number goes up
to 4; but you've left out 9 more eyewitnesses to the Book of Mormon. While only
four claimed to have seen the angel (you didn't include Joseph Smith), 8 more
testified that they held the plates and examined them with their own eyes. That
brings it up to 12 vs. 4 in favor of the Book of Mormon.
As kind of an aside, I've studied Joseph Smith a great deal and I don't find
anything embarrassing--unless I believe everything everybody claims about him;
but I don't do that for either Bill Clinton or George W. Bush. I investigate it
and weigh it with a critical and reasonable eye and find that after you remove
the emotion and bias, the truth is left.