The big difference is the soundboard!

Archtop guitar
A true archtop starts with a slab of wood 2-3 inches thick.  It takes a great deal of labor and a high degree of skill to whittle that slab down to about 3/4" thick into a dish configuration.   Orville Gibson developed the first ones in the 1890s.  They became popular in the 1930's when jazz bands found that they made a great deal more volume than available flattops. The dish is what gave it punch; the string configuration adopted the Tailpiece approach like violins, cellos etc.  That gave it maximum volume and the "dry" clear notes with good sustain and sparse overtones... perfect for solos.  In time, amplification came along and the importance of carefully carved tops lessened.  Totally acoustic archtops are no longer produced by any of the major manufacturers. 
 

Early Gibson L-5

1942 Selmer-Macaferri 

Gypsy Hybrids
We are using the word "hybrid" to describe a guitar that has an arched (actually domed) top that starts with a thin slice of tight grain soundboard wood... around 3.5 MM, carefully braced into an "induced arch" at a 12 to 16 ft radius. 

Regular "Push-Pin" flattop guitars have a slight induced arch with a 30-40 ft radius. 

The Gypsy Hybrid is built with a tailpiece and floating bridge.  This is the most important aspect of the design.

Drawing a contrast...
I suspect that a well made Hybrid will out-project any acoustic Archtop.   

Part three Archtops... where they fit

Part four... the first Hybrids... the story behind Django's guitar!

 
Bracing transfers the energy of the bridge to the soundboard and forces the soundboard into an induced dome.

Motorized sanding dish used to create 15" domed body and its braces