Recoil is going be 15-20% more in the 06 case, pending on load. Case life ?, alot of variables there. But might expect the 444 brass to last longer.
For myself , I would ask, what kinda preformance I needed.
First what range capabilities, would I want. Then what bullet preference's do I have.
I haven't put them to a ballistic program, but expect the 338-06JDJ, too have a 100yd+ advantage over the 338 #2. (pending barrel length)
Now considering the bullet weight/construction is up to the task. This is my personal thought on an Elk round.I use 2000fps - 2000ft/lbs for terminal performance as a guideline. When a given cartridge, drops below that criteria, I don't shoot beyond that range.
Again, not having looked at data, ( I have a fair idea,as I have talked with JD on the rounds myself) the 338#2 is somewhat less than the 338-06. And the 338-06JDJ won't be far behind the 338win mag.
Dave