I have had personal experience with both Redline and Royal Purple.
RP smoothed out the shifting in the E39, after the Redline made it nearly impossible to shift.
WhenI got the E34, I just went with what was working for me in the past.
In all fairness to RL, people in the 39 forum use it to great satisfaction, so maybe my 540 is allergic.
Oh, ATF is what it calls for.