15W-40 will usually be Conventional Dino or Synthetic Blend.
5W-40 will usually be a Full Synthetic or Synthetic Blend.
The W number is a cold cranking and pumping standard that oils meet. 15W is usually pretty good down to 15*F. 5W is usually okay down to -15*F. Any lower and you need a 0W
Normally the Dino Conventional Oils are fine at factory service intervals. You can go longer with synthetics. If you dont deal with low temperatures a good 15W-40 Conventional like Chevron Delo 400, Mobil Delvac 1300, Motocraft Diesel.
Just make sure you always buy a HDEO (Diesel) as there are a few gasoline only 15W-40 out there and a fair number of 5W-40 Synthetic Gasoline Only Oils.
The 6.0 Powerstoke uses oil to run the injectors.. They can be picky about the oils they like. You may want to consult some of the internet forums for Powerstroke Enthusiast to see what the latest word is on preferred oils.