What's the difference? I want to know.
Simply put, statistical evidence is a piece of information taken from, say, a study or a survey. For example, if I wanted to substantiate a point that smoking is linked to lung cancer, I'd provide a stat that might say something like "30% of smokers contract lung cancer during their lives, compared to a mere 5% of non-smokers". While this wouldn't prove my argument beyond dispute, it'd certainly help to back up my claim.
Anecdotal evidence, on the other hand, would be more along the lines of "My friend Bill used to smoke, and got lung cancer." Anecdotal evidence is seldom seen as sufficient to justify an argument. It can be used as an illustration of a point, but I could list all the individual cases of lung cancer in smokers that I wanted and it would do very little to further my point, largely because it can be countered in two very simple ways:
1. "Really? Well my friend Jim had been smoking since the age of 12 and was fit as a fiddle until the age of 86, when that bus ran him over."
2. "Prove that Bill wouldn't have got lung cancer anyway."
In this case, Bob's listed a dozen or so gay serial killers and seems to be under the impression that it proves his theory that homosexuality is linked to criminality. In actual fact it gives a very skewed picture, because of the hundreds of heterosexual serial killers, and the millions of non-murderous homosexuals. If he actually wanted to make a point that anyone but his own little cadre-cult-congregation would have even a modicum of respect for, he would have to produce a statistic from a reputable source that actually showed a trend for mass murder in homosexuals.