Why would some flights use props instead of jets?
I believe this question is answered here and a nice comparison can be found here but the short answer is efficiency. If memory serves jets gain their efficiency at high altitude moving fast and generally over a long distance. If you are going on a short hop turbo props will be more efficient overall. This chart provides a nice outline of the difference in efficiency. 



As for large piston pounders I am not sure of the efficiency but I would think the cost of keeping one running is high simply based on their age (no one is really making big piston planes anymore as far as i know). History channel has a nice show "Ice Pilots NWT" about a freight/passenger airline that still runs DC-3's and the general issues they have with them many of which is related to finding parts. 

That being said not all airlines had the money to jump right into jets when they came out. Lots of turbo-props are still flown simply because there is no reason to replace them.