[1] https://en.wikipedia.org/wiki/List_of_cities_in_the_European...
More people live in Munich's metropolitan area (i.e. where underground and overground take you) than Berlin. Still, Berlin feels like a proper city and Munich like a large village.
Berlin vs Munich is where your metric (people who live inside city boundaries) works to describe the metropolitan effect.
Paris, on the other hand, is on another level entirely. When you travel from Paris to Berlin, Berlin feels like a small town. And here, the metric of people who live inside city boundaries just doesn't describe the feeling of the cities at all.
Often there are cultural aspects at play too. I live in London. I also live in Croydon - it'd be one of the largest cities in the UK in its own right if it was separate to London (and on more than one occasion the council has tried to make that happen). Most of the borough is part of the same urban area, but some are fairly well separated. Several parts of the borough are really separate towns, separated not just from London but from Croydon by "relatively rural" land (by our standards), with their own town centers, train stations, and culturally distinct.
All of this is within the administrative city limits of Greater London ("London" doesn't really exist as an entity of its own - and before anyone else says City of London, that's one tiny constituent part of Greater London - nobody means City when they say London)
So when you say Berlin, everything might be within city limits, when you say London, odds are you wouldn't think of every part within the actual city limits as part of it, nor even a city, but the Greater London urban area includes tendrils extending beyond Greater London too that nobody other than perhaps extra audacious real estate agents would call London. When you say Paris, odds are you might include some parts beyond the formal city limits but very unlikely the entire urban area.
Even then, you won't even get people living each place to agree where the line goes.
For this discussion (cultural centers of Europe), Greater Paris, Greater London and Berlin (they have roughly similar areas) are what you want to compare, and Berlin is clearly the smallest one population-wise out of these three (and it's not even close).
If we want to shorten the name of City of London, the short form is the City, not London. The only people who ever calls City by the name of London is people who have just learnt of the oddity.
Greater London makes up the formal boundaries of London. It's the legal and administrative boundary, and the city limits of London. Unusually, unlike the city limits of many other cities, you'll find plenty of people including people who live here who not quite consider the outer parts to be part of London. People where I live sometimes still consider it part of Surrey even though it's been part of London since 1965.
There are forests and agricultural areas almost entirely separating parts of the borough I live in from the rest of London.
Yet in other areas, the Greater London urban area expands well past what anyone would call London, including e.g. entirely separate towns in other counties, like Watford in Hertfordshire, Gravesend in Kent, Epsom and Guildford in Surrey.
So yes, these comparisons are tricky but that is the point.
E.g culturally, London is likely reasonably described as smaller than it's city limits, while indeed some other cities are often larger than them, but rarely as large as the urban area they are within. It's extremely common for towns on the outskirts of large cities to have their own separate identities and not be considered part of the adjoining city, but still form part of the same urban area.
Depending on what you want to compare and which cities you are comparing, different measures will be more or less appropriate, and may require different considerations.
This seems almost obnoxiously confusing when talking online to people from all over the world.
[And, yes, this means there was a 14 year period when the UK had a capital without a government, nor indeed any administrative unit - effectively "(Greater) London" as a political and administrative entity didn't exist during that period -, largely for political reasons - Thatchers government was strongly at odds with the then particularly left wing Greater London Council]
But really, the reason for contracting City of London to "City" rather than London is to minimise confusion, because it means London fairly unambiguously, though not entirely, refers to Greater London.
You can have these differences within one city as well, on the district level or even individual streets.
Paris has the specificity of having small limits for the city proper but it does not make sense to use that metric for comparison because nowadays the city only stops at the administrative limits for adminsitrative purposes and nothing else. You won't even notice you've crossed the limit if not for the ring road.
In fact, Moscow is also larger than Berlin however you look at it we we're talking about "continental Europe" (which I take as a way to exclude London, which is also larger than Berlin...).
It might well still be the biggest in the EU if you drew limits based on what people considered part of the city - I don't know - but it certainly would not be as big as its urban area.
In fact, I'd argue you're unlikely to find any major city anywhere in the world where most people would agree that every part of the outer boundaries of the urban area are part of "the city" (or even "a city"; parts of urban areas will still often be considered fairly rural by those who live there or in the nearby city) even in a loose colloquial or cultural sense. Even coming close would be exceedingly rare. This because the ways urban areas are designated by design tends to include commuter regions far outside, with their own identities, and often very separated from the biggest city in the urban area.
So while going by city limits will be misleading, so will going by urban area. Unfortunately, no single metric will be accurate for these things.
I live outside of London, howver you define 'London', but still in London's area of influence considering how many people commute into London from here every day.
At the same time it's specifically meant to be aligned to OECD and Eurostats definition of a Functional Urban Area, which is a definition meant to ensure comparable statistics across countries, which neither the "old style" urban nor metropolitan area terms provide...
Which really just goes back to the main point that you can get pretty much whichever result you want here unless you narrow it down to the specific criteria that actually matter to you...