"not as" versus "less"

Solution 1:

These are two completely different constructions. They're semantically related, but they have quite different syntax. As has been pointed out, they're not strictly comparable, so one should expect they wouldn't show up with the same Ngram distribution. If they did, that would be significant; but the opposite isn't. Variation is always the null hypothesis in language.

• The as...as construction, called the Equative
  (there are two varieties, the "exactly as..as" and the "at least as..as" equative)
• The more/less construction, called the Comparative.
  Both equative and comparative are in the same semantic territory as
• The most/least construction, called the Superlative.

Semantically, these are all very complex, involving at least two different propositions, both quantified, and a comparison between them. In addition, all of these constructions (except the "exactly as..as" equative) are Negative triggers, in that they allow NPIs like ever:

• He's as fit as I ever expected him to be.
  (but only for the "at least as..as" case:
  • He's at least as fit as I ever expected him to be.
  • *He's exactly as fit as I ever expected him to be. )
• He's fitter than I ever expected him to be.
• He's the fittest one I ever saw.

That is, logically, they all contain at least one negative and two quantifiers; this is industrial-strength logic, rife with peculiarities and ambiguities. Anyone wishing to propose a logical structure is welcome to do so; it's been done before, many times, but never successfully, to my knowledge.

This is true without any not, or never, or any other overt negatives in the sentence. Adding an overt negative to any of these constructions results in two negatives and two quantifiers, and at this point most people lose track of what's going on, usually resulting in overnegation of some kind.

I'm not even going to mention the syntactic peculiarities; semantics is more than enough.

EDIT: I have dealt with some of the syntactic peculiarities here, by request.