This one takes some time to get used to both phrasings in order to be able to take a step back and provide the sort of objective evaluation we insist upon here at BAJTOTW. At first, “how are you going?” just sounds more like a mistake than an alternative, like somebody got the phrases “how are you doing?” and “how’s it going?” confused.
Really, though, a phrase like “I’m doing fine” is supposed to reflect the inner-state of a person, but the wording gets this wrong. That you can say “I act like everything is okay but really I’m not doing very well at all” should be, semantically, a contradiction in terms.
Jeremy’s winner: How are you going?
To a non-American, “How are you doing?” sounds like someone got “how are you going?” and “what are you doing?” confused. I didn’t realise “how are you going?” could be confusing until I said it to a non-Australian non-American the first year of grad school, and she replied excitedly that she’d just finally figured out what that meant.
Beckie’s winner: How are you going?