Both are generic spectrums... "Product of the USA" is vastly more generic then "Raised in the USA"... you couldn't possibly make "Product of the USA" a common-folk-understandable term that means what most people think it means, because the spectrum is too large.... Does it mean the chicken was born in the USA, fed only seed found in the USA, which was grown in the USA, collected by a US business/individual (with no foreign labor or equipment)... etc.... By the end, no car could ever be a product of the USA because every engine or battery needs a component or element that is often imported.
"Raised in the USA" could be meaningfully quantified in a way people can understand... for instance: "spent the last 51% of its life in the USA prior to slaughter", or to support export: "Spend the last 51% of its life in the USA, prior to being sent to slaughter, not to exceed 7 days outside the USA"
Of course, people will bicker over the 51%... I don't like that either, but it's a "simplification" of the issue to a slogan, which is what all of this is really about anyways, if we don't provide quantifiable and factual statements like M-COOL partly provies (it's still ambiguous itself on the "raised" part, I think... though I've not read the full details)
The point is, "Product of..." is essentially meaningless without added context. If I buy a McDonalds Hamburger, cooked by someone in my hometown in New Jersey, is that a "Product of New Jersey"? Sure! But also no, if the meat was ground in New York, from a cow slaughtered in Vermont but born and raised in Alberta Canada.
Short, pithy slogans are great to get people to think/feel things, but they're absolutely useless to actually explain anything. Look at how long my post is when I could have just said "You cheated!".
It's okay to import an animal, put them on a feed lot for a few days, then move them over to the slaughter house and claim "raised in the US"?