I think the Basso must have much more "trail" in the steering than the Felt. The readiness of the front to turn at the slightest provication while parked along with the sluggish response while riding both point to this. Your stem lengths and angles have little or nothing to do with the difference.
I expect the Basso has a shallower head tube angle than the Felt and possibly a fork with less rake so the trail is significantly greater. Italian bikes from the 80's tended to have slower, more stable geometry than current bikes so this is likely.
The only "cure" would be to get a fork with significantly more rake for the Basso. Rakes of 45 mm are common and, if the Basso has less than this, a fork change would solve part of the problem. You may need a fork with, say 50 mm of rake, to get close to the handling quickness of the Felt. None of this is going to be free.