I hope you enjoyed the nice little war of opinion your topic started. It's a really good question, and I figured I through in my 2 cents.
The answer is: It depends on the house.
I know, lousy answer. But here's why:
Appraisers use a numerical (math oriented) approach. That's a good way to value homes if the homes are A) typical in floor plan B) numerous in the target town C) without any "psychological" factors, such as steep lots, highway noise, poor curb appeal, tricky driveways or impeccable condition. D) Prices are stable, because appraisers use property comparisons that are 1-8 months old.
B) Realtors (at least, the good ones) all have their own methodologies, but we work with buyers, so we "see" property through their eyes, and are a lot more likely to realize that a typical appraisal value will come in too high or too low based on what the market will pay. Also, we tend to be more forward looking, because we live in the now, and not in the market of yesterday.
So, you see, each approach has its advantages. Certain houses will be much easier to appraise than others, certain houses will see the appraisal differ significantly, due to differences in the underwriter guidelines (which means different banks will force appraisers to evaluate the same property differently).
Regrettably, there is no "right" or "wrong" answer. At the end of the day, procuring a willing buyer determines market value.