Hi Mstram / Mike,
As you've said, you're familiar with the spool-up times of old. In that era we were well aware of the often quoted "7 Deadly Seconds" that it took to spool up from idle to full thrust. Airline training was VERY VERY paranoid (with good reason) in pounding this information into pilot's brains, and instituting minimum N1s on approach below certain altitudes etc.
Even on the older engines of the B707 / DC-8 / B727 etc. era, spool-up was quite lively in the upper range of RPM, as a 'ball park' figure, from about 70% N1 onwards. It was the eternal waiting from idle to about 70% N1 that was the killer (sometimes literally).
On the modern high bypass engines of my experience (CF6, CFM 56, RR Trent) spool up from idle is much much faster, with acceleration at the top end of the speed range about the same as before. This is a bit subjective, I never timed it, but then, nor did the airline operators either, because no longer was anyone concerned sufficiently to publish spool-up times, or quote minimum altitudes for idle thrust (Not withstanding good operating policy of establishing stabilised approach criteria). This has come about by the use of much improved surge / bleed valves, and in particular, re-scheduling the Fuel Control Unit to a Flight Idle setting much above Ground Idle. I've had an FCU (or is it a FCU) fail to ground mode in flight, and the acceleration qualities were just as lousy as in the old days. On the 'down side' of this high Flight Idle, is that the aircraft can be a real b!tch to get down if you're a bit hot and high, and that pilots are now much more adventurous in accepting low altitude sink rates, knowing that a rapid thrust response can save their skins.
Turbo-prop acceleration depends on the type of engine. There are 2 types, variable RPM engines, like the RR Dart, or constant speed engines like the Allison (P3, Electra, C130) or Garret (Metro, Jetstream etc.).
Acceleration for the variable speed engine comes about by 'fining off' the propeller as the fuel flow is increased (much like the piston engine / constant speed prop). Rapid power increases in the RR Dart could cause the prop to fine-off excessively quickly, resulting in huge drag increase just when you needed power. The throttles had to be carefully advanced, making sure that torque increased as RPM rose.
On the other hand, constant speed engines (literally that, the engine is always at the same speed) are a pilot's dream, the power is available as quickly as you can push the power levers up, there's no acceleration required - Instant Response!
All a bit subjective - I speak for the engines I've operated, others may tell a different story.