From my understanding and very recent interaction with an appraiser for a large national lender- Appraisals are just comparing apples to apples: sq. footage, property specs- baths/beds, basic features.
So- I'm going to actually disagree slightly and say that appraisals can also be on the lower end of what you'll see with comps. And if you're talking about taxing offices, then the appraisals would come in on the higher end most likely as that would benefit the city or town.
Comps tend to be much more realistic as to what is going on in the market currently. In the case that my Mother's neighbor sold their very similar home for a certain amount, you get an idea of what actually sells- not a speculation of the value based on statistics.
With that said, comps can be emotion driven as buyers can fall in love and must have a property- potentially driving the price higher.
I usually look at the appraisal and comps and come to a range and estimate on my own.