Is the differential between the forward and aft CG limits indicative of the overall stability of an airplane?
Normally, the aft limit is governed by static stability, while the forward limit is governed by the elevator control capacity (but sometimes, dynamic stability: excessive static stability may cause oscillations).

So, a narrow CG range would rather suggest that the elevator and/or trim capacity is not sufficient to cope with the more forward CG.

However, in practice there may be other reasons for restricting the range. For example, it may simply be impossible to load the aircraft (without exceeding the station load limits) in such a way as to put CG out of the defined range. I think C152 is close to that. Or, say, the stall or spin characteristics are unsatisfactory, so the aft limit may be restricted further than what normal stability dictates.

Needless to say, artificial stability augmentation (including FBW) may broaden the CG range, primarily by affording a more relaxed aft limit.