Turboprops are more effecient on fuel consumption (most of the air mass moved is cold air, so you're not wasting gas heating up the flight levels)

Turbofans (the big fan moves a lot of cold air) are more effecient than pure turbojets (ALL the thrust is 800 degrees C, lots of wasted heat).

Turboprops are more effecient on short routes, but this advantage drops off as the leg length increases...the turboprop takes more time to fly the route than an RJ:
1) You have to pay the crews a longer block
2) You have to pay the mortgage on the airplane, but you get to use it on fewer legs each day


Passenger preference was the reason the RJ was introduced...the PAX don't like noisy props, and they like shorter flight times. Oil was a lot cheaper when this decision was made. The Q400 is a great airplane: very quiet and very fast, and the interior is the same as a CRJ.

The explosive growth of the RJ post-911 was driven not by airplane effeciency but by lower labor costs and the ability of the RJ to cover mainline routes. Most RJ flying today could not be done by t-props (SLC to ORD in a typical Tprop would take 5+ hours and require a fuel stop)