好きな食べ物は食べた
好物は食べた
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"?
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):
好きな食べ物/好物:ピザ、ちゃんこ鍋、ラーメン
「好物」can be used to refer to not just food, but drink too.
15世紀のイタリアに生きたレオナルド・ダ・ヴィンチはワインが大好物だったと聞いても決して意外ではないでしょう。(source)
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:
自宅で好物の料理を作りましょう
妹が俺の好物のバウムクーヘンを作ってくれた。やった!
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.