I imagine when the phrase was coined (oh so long ago), it was probably true. Today, I see very little similarity to Paris. But the phrase lives on. Now it's just one of those things people say without knowing why they say it.
I've never been to Paris, so I wouldn't know. When I lived in Spain, I was just naturally turned off by the prospect of having to deal with getting around in foreign countries where I would definitely be labeled as a foreigner. In Spain, most strangers I met couldn't tell I was American because I looked like everyone else. People I know who went to Paris have had interesting experiences. Like when my sister tried to speak French to people (she studied it in school for about six years), they would answer her in English. However, in the airport, nobody will speak English to you. Various people have told me horror stories about the airport there. I know there are lots of things to see in Paris, but I don't have any desire to go there, mainly because it's expensive, and I don't speak French or have any interest in France. So, in my opinion, Paris must be the Buenos Aires of Europe.