A lot of good stuff has been said here. I'll toss out a few more observations.

Regarding weight, when building a weight weenie bike you don't get much savings from just one thing. Rather, you save a few modest chunks here and there and you save smaller chunks all over the place. Together they add up. There was an old backpackers' saying "Take care of the ounces and the pounds will take care of themselves." Same with bikes. What this means is that while the weight savings from a boutique steel frame may be the largest single chunk you can save, by itself it still won't amount to much. Conversely, if you spend $200 each on every lightweight component on the bike it will be wasted money if you put them on a frame pounds heavier than you might have used.

Can I feel the difference? My "good" bikes weigh between 23 and 25lbs, more or less. I can feel the difference when I pick them up. When I ride they feel different in how they accelerate but that could be as much due to the wheels and tires as to the total weight. They all handle differently too but that's probably due to geometry.

I weigh about 160lbs and on hills I prefer to spin rather than mash. I never feel BB flex. I haven't ridden the 531c Gazelle yet but I suspect I won't feel any flex in that either.

I have noticed frame, or at least fork, responsiveness between bikes. On my previous commute there was a serious serious serious downhill, so serious that one could burn through brake pads at the bottom. I ran that hill on at least five different bikes. The Masi was quite in its element. I don't recall any particular behavior (of the bike, not me - my behavior was all about how and when to apply the brakes!) of the Raleigh, Bianchi, or Centurion. The UO8 on the other hand was much less well-connected to the road surface. Of course the UO8 isn't even close to being in the same class. Its greater frame weight might have stabilized it, as per sports car theory of sprung to unsprung weight ratio. It has similar tires and alloy wheels as the R, B, and C. But it was clearly not happy running that surface at those speeds.

The bottom line is that the frame is just one component of a system. No single item matters much by itself but all the parts contribute. There is no "I" in "team". No "I" in "bicycle". No, wait, make that no "I" in "bike". No, no, um, no "I" in "component and frame". Yeah, that must be it.