It's definitely not as big as those in terms of surface area. But it's quite spread out and what counts as the "center" is a very loosely defined notion that is actually quite large compared to all those cities.
There's a ring of sbahn commuter rail around the center. From east to west that's about 16km and from north to south about 10km. Anything inside that could definitely be considered as the center. Walking east to west would take about three hours or so. You'll pass through a lot of interesting neighborhoods, each with their own little centers. You'll pass lots of landmarks. The former east and west berlin "centers" are about 9 km apart. A lot of the traditional landmarks and hotspots are spread out throughout that zone. And then you have a lot of gentrified spots that are becoming hotspots in their own right.
I use the word center loosely of course because there really is no such thing in Berlin. It's all spread out over a huge area. There are probably about well over a dozen areas that can lay claim to being a center of something. And frankly, most of the interesting bits are outside of what the tourists flock to these days.
Outside the ring, the city continues in pretty much all directions for quite some distance. And some of those areas are quite nice as well. But most would not consider that the center. I've lived here for about fifteen years and there are huge parts of the city that I've simply never even been to because it would take like an hour plus to get there and there isn't much in terms of landmarks, etc. to draw me there.
Technically Berlin is actually a city state (within the federation of Germany) that includes the capital and a few suburbs. Total population is still smaller than it was before WW II (3.5M people vs 4M people then). So there's a lot of open space, huge parks, two decommissioned airports (Tempelhof, Tegel), etc. all within the city limits. Tempelhof is huge. About 2km by 2km of open space in the middle of a big city with two decomissioned runways. It was the site of the cold war air bridge. You have Kreuzberg to the north, Neuköln to the east and Alt Tempelhof just outside the ring on the south west side. And that's just one corner of the city. All in former west Berlin.
The population is growing for the last decades at a pretty decent rate (about 50K new people per year or so). But it will take some time to catch up to pre WW II era levels.