Over the years (82 of them!) Batman has dealt with a lot of people, and created a lot of mystery around himself. In doing so, he earned many a moniker.
I’ve always liked it when Ra’s called him detective. It makes it seem like they have something different between them in comparison to Batman’s other rogues. It’s obviously not definitive, but it’s my favorite of his nicknames.
I voted Ras’s “Detective,” not only because, as @Rip_Rubbler points out, it shows a familiarity between Bruce and Ras, but implies “World’s Greatest Detective,” one of my favorite aspects of Bats -a moniker I also love. I’m looking forward to “The Batman,” which is supposed to finally represent this side of The Dark Knight on film, something sorely missing in the big screen adaptations.
Dark Knight has always been my favorite nickname for Batman ever since I first encountered it in the Steve Englehart run of Detective Comics. If I remember right, that was the first time it had been used since the Golden Age!
I am also in favor of Ra’s simple Detective. Beyond the relevance for their relationship, it also reflects Ra’s respect for Tim Drake. He’d never called Dick or Jason (or Damian) “detective,” but when he is bested by Tim and uses the term, it carries the weight of 70 years of precedent.