The only thing I have to offer in the way of data is some quick numbers I dug up on J. D. Martinez as a member of the Red Sox.
In his 1 + seasons with the team, J. D. has been used almost equally in the 3 and 4 spots, which is sort of interesting in itself.
Total PA 882
3 spot 432
4 spot 447
9 spot 3 (don't remember this)
OPS
3 spot .967
4 spot 1.024
RBI
3 spot 90
4 spot 72
So in this one very isolated, small-sample case, it would appear that JD has had more RBI opportunities in the 3 spot, since he has driven in more runs with a lower OPS.
Not drawing any conclusions from one small-sample case, obviously. Just throwing it out there, as the saying goes.