I'm wondering what the best sentence is between those two. What is the most grammatically correct one ? Which one sounds better to you ? Is one more commonly used in one country ? (exemple : UK vs US) ?
Basically, there is no context, what would people say most naturally : "This is my picture of Paris" or "This is my Paris' picture" ? (Paris being a generic word here, no mention of any monument or specific place)
A "picture of Paris" suggests to me a picture whose subject is Paris. It may depict a representative part of, or scene from, the city. It could be an aerial view of the whole, or of a representative part, of the city.
In a "Paris picture", the relationship between the city and the picture is more vaguely defined. It could, for example, be a picture of Big Ben that was held in a vault in Paris for a long period.