From what I know, both というか and というより are used to correct or improve on a previous statement, but are there any differences between them? For example, are the following two sentences different?
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Based on my personal reflection, when people utter AというかB they tend not to prepare what they exactly want to say as B when they start to say it; e.g. your friend suddenly see something and say "That's A!", then you see it too and find it not as much A at once, so you just start to utter 「Aというか...」 while searching for whatever word it really seems to you. The particle か represents such kind of hesitation.
On the other hand, I think they tend to use AというよりB when they are already confident of B, or at least have something in their mind when they start to say this phrase.
You can also put というか in the beginning of sentence to mean "by the way" or "apart from that" in very casual conversation. というより does not have this usage but you have それより as a synonym to this except it has less colloquial vibe.