むしろ

1. 1Rather, more accurately: B describes the situation better than A.Ex. 1
2. 2Rather, preferably: B is judged better or more important than A.Ex. 2
3. 3If anything: the actual outcome leans toward B, the opposite of what was expected (e.g. 薬を飲んだら、むしろ具合が悪くなった).

Used in both speech and writing to correct or refine a comparison, typically in the frames AよりむしろB or AというよりむしろB. It suggests the listener might have expected A. Plain より〜ほうが makes a neutral comparison, while かえって stresses that a result reversed the intended effect. むしろ can describe such outcomes too, framing them as "if anything."

• というよりN3「というより」 follows A and is used only to correct a description, evaluation, or purpose/reason; unlike 「むしろ」, it cannot choose between two courses of action, and it can also begin a sentence as a conjunction. The two often combine as 「AというよりむしろB」.
• ほうがましだN1「ほうがましだ」 works as a predicate and is used only to pick the lesser evil between two undesirable options, with a negative, resigned tone, and it often pairs with 「くらいなら」. The B part of 「むしろ」 can be something good, and 「むしろ」 can also correct a statement; the two can be used together.
• かえってN2「かえって」 presupposes an expectation and signals a result contrary to that expectation or to common sense, often paired with 「〜たら」, 「〜のに」, or 「〜ために」 and carrying a tone of surprise or frustration. It does not express comparison or choice between two things.
• より〜ほうがN5「より〜ほうが」 is a general comparison that can compare degree or express an evaluation, with no corrective nuance. It can combine as 「AよりむしろBほうが」, which still works without 「むしろ」 but sounds weaker, while 「というよりむしろ」 cannot be replaced with it.

というより rephrases a description, and むしろ often follows it to stress the more accurate choice. より〜ほうが is a neutral comparison, and ほうがましだ picks the lesser of two bad options. かえって emphasizes an outcome reversing the intended effect, whereas むしろ frames B as the better description or choice, including for unexpected outcomes.