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I suspect this is correct. I find softened onions preferably for a number of uses. Caramelized onions can be too sweet, and soggy/limp. I've even found that leaving a trace of crunch is better in many cases (eg beef bolognese). But don't listen to me, I've never really figured out the difference between cooked yellow, white, and sweet onions, and just buy whatever is available and has the least mold and soft spots. E…
tl;dr When cooking, use yellow. They're cheaper and you need less. --- Yellow onions have a stronger flavor, even after cooking. (Though cooking of course lessen it a lot.) White and sweet are essentially the same, with the latter being slightly sweeter. In the end they do taste similar cooked. Biggest difference is price. Yellow is usually 20% cheaper than white and 40% cheaper than sweet.
Red onions are a different flavor profile altogether, and best for some (not all!) Mediterranean or Mexican dishes, or smoked salmon (NOT lox - yuck!) on a bagel with cream cheese and capers.