A long time ago in a land.........
It began when jets were true turbo jets (1940s-1960s) not turbo fans which are mechanically (especially with the forthcoming GTF) actually very similar to turbo props as they derive most of the thrust from the by-pass section rather than the core.
The book "Handling the big jets" by DP Davies (RIP) details how "old jets" with their swept wings heavier all up weights, greater momentum and no slipstream effects were difficult to go down and slow down and needed high power against drag on the approach (flight path stability sometimes poorly called "speed stability").
Old Jets also had very long engine spool up times which combined with the way a turbo jet produced thrust at low airspeeds meant the go-around from a low thrust setting could be fraught with sink and back of the drag curve speed control problems.
Today's engine spool up times are faster and the huge By-Pass fan effectively bites the air more like a propellor at low airspeeds than the old turbo jets ever did - this makes modern jet airliners more flight path stable on approach.
Then there's high altitude operations - sadly many modern pilots aren't aware of the changes in momentum (TAS) and it's effect on manoeuvrability or the real meaning of coffin corner (Stall and Mach Buffet variation with weight and altitude). The AF447 disaster will hopefully mean more pilots read up on it. Some airlines refuse to let their pilots fly much above FL350 because of some unwise operators trying to climb too early when far too heavy.
Turbo props operate in the worst weather into shorter runways. They face far more icing challenges and have more engine controls to consider than jet pilots.
The Q400 is pretty fast for a TP and on short sectors can match many medium jets in terms of flight time.
Without the flight testing of ILS/DME/VOR/NDB/MLS/Radar/SIDS/STARS beyond the limits of the average airline flight, the current Air Traffic system would be very unreliable. Turbo props such as specially modified B200 King Airs (Aerodata GmbH and Cobham Flight Inspection) are used to test these to extremely high accuracy. Auto Pilots don't have the response rate to calibrate a 50 foot roll out guidance for an airliner's CAT3 ILS AutoLand so these are flown multi crew manually at 180KIAS gear up, usually at night with a laser tracker for ILS reference. These pilots have very good manual flying skills and each crew tests around 55 airports per year in the EU.
But would a calibration pilot get an interview with a "jet" operator? In the old days yes! Now some (less enlightened) airlines just see the B200 hours as light aircraft ops and cadets are just far more profitable.