Why do aircraft models end their life as freighters?
Passenger operations are overwhelmingly scheduled whereas cargo is on demand and thus less easy to plan. The upside: A cargo plane crew will fly quite diverse routes. The downside: Capacity utilisation is worse. This shifts the balance of cost such that fixed cost must be lower than what is possible with scheduled services. As a consequence, older aircraft with lower depreciation cost are preferred. With them it is less costly if they don't move for some hours or even days.

Caveat: Integrators (freight companies which ship door-to-door like FedEx or UPS) run their freighter fleet like a scheduled service, but still their utilisation is lower. Please see @TomMcW's answer for a detailed analysis.

Operating cost are more important when the aircraft flies as much as technically possible. Especially low cost airlines need to operate hardware with the lowest operating cost possible so they survive the next price war. Premium airlines also have a need for the newest planes: This makes them look premium and more safe. Cargo operators have no such incentive to prefer the newest airplanes; they profit from the need of passenger airlines to sell their older hardware off.

Next caveat: Older airplanes are at least as reliable as new ones when maintained well. The need of premium airlines for newer planes is only to impress their ignorant customers, not to increase real reliability numbers.

The Economist wrote in April 2013 about Norwegian Air Shuttle:


  As fuel prices soared in the mid-2000s, and competition from the likes
  of Ryanair and easyJet intensified, Mr Kjos realised that the only
  route to survival was to buy lots of new, fuel-efficient planes to
  achieve economies of scale, and to base some of them in cheaper
  countries. Boeing and Airbus are straining to keep up with booming
  demand for new aircraft, so by reserving a large chunk of their
  delivery slots NAS is denying potential rivals the chance to refresh
  their fleets with better planes.


If an airline is large enough, ordering new aircraft has the added benefit of saturating supply and denying the same aircraft to its competitors. If oil prices are high, this airline will have won the price war before it started in earnest.