This is obviously subjective and just my opinion, but let me add more depth to justify why I hold that opinion a bit more.
Facilities-wise I was talking about lack of seats, lack of spacious and modern and frankly sometimes clean bathrooms, lack of sufficient staff doing things like passport checking and security, lack of physical space for movement of people through the airport, lack of food/drink and shopping quality and variety, particularly past security. All of these apply to both, with Schonefeld being noticeably worse on every point.
Capacity - All I can say is that at both, there are slow-moving queues of people at gates that restrict the movement of people trying to get to other gates. There is more throughput of people now than the airports were designed for - they're tautologically over capacity - if they weren't then this wouldn't happen, as it doesn't at most other airports.
Public transport - this one's subjective and depends on usecase, and I'm not claiming it's terrible. It works, and sure it's relatively quick. But it's exactly those connections (from Tegel) that bring the inconvenience for two reasons - the first is that it's more difficult to navigate to the center having to make connections if you don't know the system (i.e. for tourists). The second is if you have heavy luggage - it's really not convenient at all to lug bags onto and off of connections, especially buses. If you're a local who knows the networks and you're doing a short flight with hand luggage, I agree that in that usecase it's fine.
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A bit meta now: I think it's amazing and I'm genuinely pleased to see that you're not only disagreeing with my opinions, but coming to the defence of these airports and outwardly saying they're really good, along with other commenters. I worded my original comment quite strongly and matter-of-factly because I honestly thought that 'everyone' would hold broadly the same views. Anecdotally, I've never talked to anyone living in Berlin who disagreed with me on any of this, and I've never imagined whilst being in either of these airports that anyone else there could be thinking 'this is great'. I'm amazed to see how wrong I was, and I love to be exposed to the breadth of opinions that exist out there, through forums like HN, just because the scale of the internet allows them to surface. Always love to have a good debate about such things, it makes me remember the counter points I'm overlooking and/or discover new ones and rethink my original opinions a bit.