Everyone has their own opinion on this so expect 100 different versions.
My '03s are work trucks. I change the engine oil every 5k miles and run Rotella. The diffs were changed to Amsoil synthetic at 10k miles and will be changed every 50k after that. I also change the t-case fluid out to Amsoil synthetic ATF on the exact same intervals. I run dino oil in the auto transmissions because they get flushed every 25k anyway. My thinking is that the fluids like engine oil and transmission fluid, that get changed on regular intervals are not in need of the extra protection the synthetics give, especially considering the cost. My only evidence that this plan works is the 240k mile '99 PSD. The auto transmission in those was supposedly fragile. Mine went 200k easy on dino oil. This is also with everyday 15k lb towing and plowing snow on a 10 acre lot in the winter. I also waited until 200k before a complete rear end rebuild. At 200k I did the rear and the transmission as preventative items, not because they had failed. That truck still works hard and has been problem free.
I do use Amsoil in a bunch of my vehicles. I have never had any problems but then who has actually had lubricant related failures they can prove? Synthetic in the transmission might be a good idea if you work it really hard. Still I run dino and haven't had a problem even with daily heavy loads and contruction site deliverys (ie muddy, rough and ugly).