This is a great topic. I sure wish I knew just what made a "great" bike, vs just "good", or even "meh". I suspect most of it comes down to tires, and then after that fit, and maybe a distant third, geometry or frame tubing.
As an example, probably my best bike is a 1976 Centurion Semi Pro. Nice light Tange #1 tubing, and pretty standard 70's stage race geometry - 72.5 degree parallel head and seat tubes. When I bought it, it was shod in 27x1 1/4" tires that had almost fossilized. They weren't cracked and didn't have any sidewall issues, so I left them on for the first few rides. Boy, what dogs those tires were. If you had filled them with water, and frozen them, I don't know if I would have been able to tell the difference. If I hadn't swapped them for new Paselas, I'm sure I would have sold the bike in short order. After the swap, it was like riding a new bike. Maybe not the fastest, or nimblest ride, but very nice. Later, I finished building up a tubular wheelset, and put some nice Schwalbe One 28mm tubulars on there. Wow, now it's like a rocket. Very nimble, but still smooth riding. The bike just begs to go faster.

In contrast, I also have a 1976 Centurion Pro Tour. 2 cm taller in the seat tube, but the top tube and all angles / fork rake are the same. The tubing is supposedly the same, but I suspect maybe a bit thicker on this taller model. The only difference is it still uses the 27"x1 1/4" Paselas, and the stem is about a cm longer. It's still a very nice riding bike, but subjectively, it feels much heavier, and not as lively. Without weighing the frame, I can't really tell if it's the tires, heavier tubing, or the slightly more stretched out riding position. (The bike does weigh about 1.5 lbs more, but that is about in line with the heavier tires, and slightly taller frame.) I really should throw on the tubular wheelset, and see what sort of difference that makes.

Ultimately, the biggest takeaways I've found is that crappy tires make for a crappy riding bike, while really nice, supple tires will make almost anything ride better. Past that, I'm sure geometry and frame tubing make a difference too, but I suspect it isn't nearly as great as many seem to think it is. (I read an old article where they had 7 bikes made up of different Columbus tubing sets, but were otherwise identical. Many of the riders couldn't reliably tell them apart, and of those that could, the ones they liked the best were usually the mid grade tubing. The really heavy / stiff, and super light flexible ones weren't as popular.)