I'm guessing you mean more compelling for adults and not adults only.
I'd start by aging the girls up a few grades and drop the cutesy junior high stuff. Let the characters already be maturing.
Make Usagi and Mamoru closer of age to avoid the usual stuff with that since more adults will be watching.
Do Chibi Usa in R, but never hear from her after that.
Chibi Usa in the manga has some intense, emotional scenes, but overall she's still the annoying kid character. If they keep her around, age her up too, closer to Usagi. Get rid of the Chibi Usa crush, it's honestly so off-putting. Did anyone ever enjoy it?
Give the villains more meaningful deaths. To make the manga appeal to adults, it's gonna need plot and character development.
Make us hate the villains. Koan burning nuns and Demande choking kids are horrible events, but give us depth and let us explore their psyches.
The manga gets dark and horrific...but it's not really that deep.
Foreshadow. Don't throw in stuff on a whim as Naoko did in Dream Arc!
Invest us in the lives of the Senshi. Some homelife, some school drama. Maybe take some pages from ABC's "Once Upon a Time" and let the girls unlock memories showing flashbacks from the Silver Millenium and why each girl became what they are. Then show these memories unlock potential in this life.