What is the difference between むしろ and かえって?

Question

"病人のほうが[むしろ/かえって]しっかりしている。"

"三月のほうが[むしろ/かえって]寒かった。"

"強い男性より、[むしろ/かえって]優しい男性が好きだ。"

How to know when both work and when only one can work ?

Answer 1

1) 病人{びょうにん}のほうが[むしろ/かえって]しっかりしている。

2) 三月{さんがつ}のほうが[むしろ/かえって]寒{さむ}かった。

3) 強{つよ}い男性{だんせい}より、[むしろ/かえって]優{やさ}しい男性が好{す}きだ。

With 1) and 2), either 「むしろ」 or 「かえって」 can be used. For 3), however, only using 「むしろ」 would be correct.

That is, of course, unless you have in mind extremely peculiar contexts/situations for those utterances to occur in that are just beyond my imagination.

「かえって」 is mainly used to describe a result/effect that is quite opposite to one's expectations -- "on the contrary".

「むしろ」 is used to express a choice between two items -- "A rather than B".

For 1) and 2), both meaning would fit without stress.

1) People with deseases could tend to be sounder/steadier than healthy people.

2) It could be colder in March than (in February).

With 3), however, people (or rather women, in this case) like different types of men in the first place. If the speaker says she prefers gentle men to strong men, who could say that is unusual and/or it is contrary to his expectation? It is only a statement of the speaker's preference.