Is it incorrect to phrase a comparison in the following way:
Men are prone more than women to depression.
Or must the adjective always follow more?
Men are more prone than women to depression.
Since you are expressing a comparison in a particular quality between the two sets, you should use a comparative construction.
Many adjectives have natural comparative equivalents: "good" and "better," "dumb" and "dumber." However, many more adjectives lack any natural comparative; there is no such word as "beautifuler" or "proner." In such cases we form a comparative using the strict construction: more [adjective].
This can give rise to ambiguity in sentences that could be modified in other ways by including the word more. The example you present could use this modifier to indicate the frequency rather than the extent to which men are prone to depression when compared to women.
It's a moot point in this particular case due to that fact that the word prone is used here to express a potential for, rather than an actual, occurrence and therefore frequency and extent are conceptually conflated (I think Kosmonaut touched on this.) If we were to take a clearer example, this issue might be more obvious:
You might almost be able to "hear" the missing word in the second sentence:
...meaning their answers or endeavors are accurate more of the time, regardless of how much more accurate. This does not carry the same meaning as the first sentence, which states that a boy's endeavors or answers are, in general, nearer to exact or correct, regardless of how frequently. The adjective accurate is not itself being measured and compared for the two sets here, so the more modifier is used elsewhere to modify the sentence.
So, when framing a comparative sentence, one should use the standard construction of more [adjective] as though it is a single comparative adjective, provided it is the quality itself that you wish to compare. If you wish to compare the frequency of occurrence of an arbitrary but uniform quality, you do not need to modify the adjective but should otherwise modify the sentence to make clear what you are comparing. If there is little distinction between the two concepts (as in your example) then I would recommend the standard more [adjective] as it is more natural.
I would actually go with either of the two following wordings:
Both of the above sound much more natural to me than your second sentence:
Which, in turn, still sounds more natural than your first one:
Those two word orders mean two different things.
Sentence (2) means that men have a higher susceptibility to depression than women do.
Sentence (1) means that men are susceptible to depression more often than women.
So, you can't use the word order in (1) if you mean (2).