This has been hashed over dozens of times, but basically this is how it breaks down:
The Dodge with the Cummins is the best one around with a built automatic transmission or a 5 speed, as long as you don't have rust issues, seat issues, and have about $500 to rebuild the front suspension on the 4x4 models. The 5.9 Cummins is a medium duty engine in a light duty chassis, so they will run quite literally forever. The problem is it is a million mile motor in a 100,000 mile chassis. I am partial to the 12 valve Cummins engines for their simplicity, reliability, and economy, but the later 24 valve versions can run just as well but are a bit more finicky.
Service parts for the Dodges are cheap. The trucks have been around long enough that all the wear items are available, engine parts from Cummins are reasonable, and its not too often anything will need replacing. In 247k miles, the only engine parts I have replaced have been the starter, filters and a low pressure lift pump.
The Chevy can be had in two distinct flavors. The 6.5 trucks up to model year 2000 and the Duramax trucks after that. The 6.5s are a great motor if you get a good one that hasnt been railed on and don't plan on pulling the world. They are based off the older 6.2 Detroit engines, but with increased displacement and a turbocharger. They have a few issues with the electronic injector pumps, mainly centered around the Pump Mounted Driver (PMD) overheating. You can relocate the PMD off the engine and this greatly increases reliability. Parts and service on a 6.5 are at least as easy as Cummins, but as the 6.5 is a light duty diesel with indirect injection, it will never yank the way a Cummins does. The Duramax is a great engine, quiet and smooth and tons of power. The early ones had injector problems, but most have been fixed under warranty. I had one as a work truck, and it was very nice. I did not drive it enough to have any issues.
Chevys have a great style, low step-in height, good resale, and ride like a car with the IFS in front.
The Fords are really a mixed bag. The early Powerstrokes, 94-98, are awesome but down on power compared to the later ones as they do not have intercoolers. The later ones are good motors also, but seem to have more issues than the Chevy or Cummins offerings. These are complicated engines with the HUEI injection system. Lots of expensive parts to fail on them.
I wouldnt touch a 6.0 Powerstroke. Nothing but trouble. A coworker of mine has had 3 of the 6.0 liter trucks. One he rolled (not the trucks fault), next one started using coolant. Tore it down, had 7 cracked pistons and both heads were damaged also. $5500 later he was back on the road. His wife's truck has been in the shop constantly for drivability issues. Service parts are not cheap for Powerstroke engines, and most of the service has to be done with the cab off the vehicle.
After owning or having as a work truck a 1996 12 valve Cummins, 97 Powerstroke Ford, 2000 K3500 with the 6.5, and a 2001 Duramax, my pick would be the Cummins if on a budget, and the Duramax if I had Duramax Money to spend.