Re: 338/284 ??
While I cannot give you an answer from personal experience I can suggest a few things.
A while back I considered rechambering a 358 win to 358/284. I necked up the 284 and did a comparison of case volume by filling each with water. The gain would be so small that it wasn't worth the cost of a custom reamer and dies not to mention the gunsmithing costs.
You can do the same with the 338 federal vs the 338/284. Once you get the numbers for how much water each case holds find out the percentage increase for the 338/284. Then divide that number by 4 and you will get the approximate increase in velocity.
I would suggest an easier way. Make a 338 RCM. It IS exactly the same volume as the 338-06. Dies, brass are available at very reasonable prices. You will need a reamer which is approx $140 from Pacific tool and gauge. How do I know? I am in the process of making one. Waiting for the new barrel.