I think both Valuate/Estibot appraise basing on
1) how many times have people searched that term
2) how many result show for that term.
And as we know, the more common words the domain contains, the more results it will show. That is why BestThe.co.uk is high.
And I found an interesting thing. Before I flipped a domain name xxxxx.com, I appraised it at both the two sites and get $0. After I sold it and the price was published by sedo. I did a search weeks later and it shew exactly the price I sold. Funny, Huh?