I find them very similar to be honest.
A 338 loaded with 275 grain A-Frames would be good for anything bar Elephant.

Both have light recoil but the 338 is a little sharper.

I like the 9.3 because of the 5 + 1 capacity as oppossed to a normal 338 of 3 + 1.

Both very very good cartridges imo but if only one it would be the 9.3 for me.
I can push a 250 grain Woody PP at over 2600 fps which is plenty flat enough.

I guess the same can be said for the 338 that it will push a 300 grain Woody RN at 2300 fps anyday.

So after all that, I guess its :Whatever blows your hair back".