It seems to me that the only possibilities of connection are "rather than", "more than" and "less than".
If you say "they like action movies as comedies", then they like them in the same way (which is not saying something very sensible). If you say "they like action movies than comedies" a comparison term is missing (less, more).
Addition in the light of what the other answers could suggest
There has to be a reference for the proportion; the number of men has to be twice as many as something. This something could be stated before. Then there is apparently no other solution than a statement as shown below.
- Quite a few men said they liked television. Twice as many men said they liked action movies rather/more/less than comedies.
The reference can be stated after, within the sentence. For this case also the reference can be one different from one having to do with action movies and comedies.
- Twice as many men as men who said they liked television said they liked action movies rather/more/less than comedies.
However, a reference having to do with comedies is also an option. The following construction makes "as" inescapable, and it is the standard construction; repetitions seem unavoidable.
- Twice as many men [as men who said they liked comedies] (said they liked action movies).
The OP's sentence is a transformation of this standard form through inversion (braces and parentheses) and elimination (bold type).
Twice as many men [as men who said they liked comedies] (said they liked action movies).
Twice as many men (said they liked action movies)[as men who said they liked comedies].
Twice as many men said they liked action movies as comedies].
The ellipsis of "men who said they liked does not appear justified: to begin with the subject of "said" is not the same.
It is probably the incongruity that results from this transformation that is the cause of the uneasiness; personally I find the "compressed" form (also a cause of uneasiness to me) too suppressive of the usual relations.
It is in fact possible to construct a sentence in which the role of "as" is ambiguous; even though in the particular example of ambiguity that is provided below, the context is a trifle far-fetched, the undecidability stands out. This shows that sense is decided through the intermediary of the meaning of the nouns being used, which makes the initial construction a difficult one to handle in certain cases. It shows also that it is a construction that is deprived of any of the characteristics that give its unique meaning to the initial one (from which it stems).
- A small group of men said they liked reading spy stories. Twice as many men said they liked historical novels as history.