JK, I have to admit that my knowlege isn't anymore than yours. I found one load for the Taylor, 71 grs. IMR4320. I suspect the Taylor to have about a 1gr + advantage over the 338 with it's sharper shoulder and shorter neck. Who and when it was developed( 416-338), I haven't a clue.
I think, (swag) the Taylor required modification for feeding( ramp and follower), the 416-388 came about to eliminate this situation. Which could be done with a simple rebarrel job on standard length mag action.
I know this don't help you alot,,,sorry :oops:
Dave