Yes, #2 sounds odd to me. The grammar is correct and I understand the meaning of #2, but I think #1 is more common, at least where I live in the U.S.

Both actually work. People often say, "on a case by case basis" for example. So: "We'll have to evaluate these accounts on a case by case basis." Both sentences might sound better if you said, "Comfort food varies ..." instead of "Comfort food would vary ..." Saying 'varies' sounds more like a statement, whereas 'would vary', especially if the speaker stresses 'would', sounds more like a confirmation. For example: A: "I wonder if they have pizza shops here in India." B: "Probably not. The food here is a lot different than what we eat in America." A: "You're right. Comfort food would vary from culture to culture."

Does #2 sound odd?