Old vs New

The first obvious difference is the shape: 

The body is longer and the shank shorter but beak and overall length are pretty similar.  Nothing to get exited over here.

Let's take at the business end:

First notice the window is much wider in the Florida.

Notice the tip rail and tip baffle.  A thinner tip rail and much higher and longer tip baffle give the Florida piece the zip and projection that they are known for.  The thick tip and imprecise baffle choke off a lot of the sound of the modern piece.

Look at the sidewalls.  You can see how much more undercut the sidewalls are in the Florida piece.  The chamber is much wider, wider than even a modern New York STM model.  The big chamber gives a great huge hollow core to this Florida Link.  The smaller chamber (yes, it is smaller -- even though the floor is generally lower the sides are narrower to a much greater degree) of the modern piece emphasizes the middle overtones more making it a different piece.  They both have an open throat, but notice that the Florida has a true large chamber (i.e., it is larger than the bore).  The modern piece, in contrast, is a true medium chambered piece (i.e., the chamber is the same size as the bore).

Also of note is the table of the modern piece.  It's not that it's merely not flat, it's wavy.  A few strokes on the sandpaper reveal the high points:

 The obvious high points at the heel, just below the window, and just past the window mean a reed will never properly seal against this table. 

Another important difference not pictured is the depth of the floor at the back of the window, which gives an indication of the floor angle.   The Florida is rather shallower than the modern piece.  That means that the floor-table angle is much shallower in the Florida piece, giving it a better balance of sound.  The modern piece has a steeper floor, which further muffles the sound, especially in the middle and bottom end of the horn.

So a number of design differences make the modern STM a much different (and comparitively neutered) animal from the ones that you heard played in nearly every jazz recording in the 50's and 60's.

Fortunately, this can be all fixed.