Some great info here, and the explanation by J.T. is really good.
Except for the Viper, my jets were very stable in the static mode, and prolly average in the dynamic mode. If you let go of the stick the sucker tried to get back to the "trimmed" AoA.
In the Viper it tried to get back to the trimmed gee ( unlike the 'bus, we could trim to anything from minus "x" to plus "x"), but the FBW control laws ruled, and not the inherent "relaxed" static stability. The interesting thing was once we had departed and had an AoA above 30 deg, the thing exhibited its natural aero characteristics because the computers only thwarted yaw and completely cut out our rudder pedal inputs. Turned out it was very dynamically stable, and ditto for static stability. So a manual control surface command via the electrons plus the inherent pitch authority once at the extreme AoA allowed us to "rock" the beast outta the deep stall. We went thru this long ago on AF447, huh?
I never flew a big plane, but I would have liked a strong aero tendency to get back to the trimmed AoA ( not speed or attitude in the FBW genre). I think the nasal radiator folks here that landed on a boat in the middle of the ocean will agree that strong pitch stability helps a lot. The other thing would be great directional stability, especially dynamic ( thinking about dutch roll).