Which is more natural or common in writing or conversation?
Converted into English, is this the same difference between "favorite thing to eat" and "favorite food"?
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There are some differences in meaning and usage between the two terms.
In some contexts they are interchangeable. For example, I could write in my dating app プロフ(profile):
「好物」can be used to refer to not just food, but drink too.
It should come as no surprise that wine was a favorite of Leonardo Da Vinci, who lived in 15th century Italy.
「好物」can also be used as a prepositive/attributive noun to modify another noun in a noun phrase:
By the way, your sentences are grammatical but sound a bit strange with the topic marker 「は」. It seems you are saying you ate the food you liked and left out the stuff you didn't like.