What is the airplane with the best flying characteristics?
First, let's get a little perspective
Stick and Rudder was written in the early days of aviation. To a modern reader, things were really weird back in the early days of aviation.

For a while, air traffic control was a guy sitting in lawn chair next to the runway waving a big flag that said &quot;GO&quot;.
Parts on the plane just failed.  Planes would crash on their way back from bombing Hitler, a truck full of mechanics would come out to bolt on some (hopefully) new parts, and then they'd take back off in the crashed airplane to go bomb Hitler some more.
One time, the Allies bombed Switzerland by mistake. This was a world where more than one airplane could miss not only a target, but the entire country.

The kinds of things that went on in those days as a matter of routine would send any modern-day NTSB investigator into full-blown panic attacks.
What I'm getting at here is that it's a mistake to judge Stick and Rudder by modern standards.  This is not the equivalent of brain surgery.  You have to think of this as a surgeon just trying to get other surgeons to wash their hands with soap before they operate.
Now on to your questions

Have aircraft flying characteristics improved?

Yes. One example out of many:  Cuffed wings.

How much have they improved?

Enough that Wolfgang didn't need to write a second book.

And what airplanes have we built that have the best flying characteristics (which are the &quot;best-behaved&quot;)?

An Airbus flying in Normal Law.
There's a section in Stick and Rudder (page 160 in some editions) where Wolfgang says that a &quot;foolproof&quot; airplane is one in which the controls have been restricted so that the pilot is mechanically incapable of pulling the airplane to an angle of attack which will result in a stall.  Guess what?  A pilot flying in normal law can yank on elevator all day long and not stall that Airbus.
An Airbus in normal law automatically trims itself.
An Airbus in normal law automatically increases power on the engines if a pilot pulls the airplane into a high angle of attack.
Some people might hesitate to put words in a dead man's mouth, but he's not here, so I'll go for it:  The best behaved airplane according to Wolfgang would be a modern-day Airbus airliner.