If there is, is it in the number of pages, the "treatment" of the theory, cost, scope, level of statistical analysis, distance?
Yes. That's why they count towards different levels of degree.
Whether the degree is conferred does not depend on the number of pages. Certainly the average number of pages in a PhD is more than in a Masters, and that is more than for Undergraduate research. However, that is out of necessity, not because the examiner counts the pages.
The intellectual and academic treatment is crucial, not just for theory, but in all the other components of the thesis-book. Harder questions are being posed and answered.
The external examiner has no knowledge of the costs involved. No thesis begins: "I spent $XXX on this research."!
Again, out of necessity, the depth of research and the area of research increase as you progress through the degrees. The level of e.g. statistical analysis perforce, must increase as you progress through the degrees, because you are tackling questions that are more difficult to nail down.
I am interpreting "distance" as being the psychological distance between you and your sequence of supervisors. All other things being constant, that _decreases_ as you progress through higher and higher degrees.
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