I can't tell you anything you may not have already surmised from clips and interviews, but I think he's going to be a bit more intense - Scorpio Rising, Aries Sun/Mercury, Mars/Pluto opposition playing out across the IC/MC (lots of action stars have Mars conjunct the MC, it's funny how cliche` and accurate that turns out lol.)
But this doesn't necessarily mean he'll bring those parts of himself to the role. Like I don't think you can see Matt Smith's Scorpio stellium in how he chose to play the Doctor as a wacky Grandpa (with tragic backstory)?
Capaldi has Neptune Rising and a Pisces Moon (plus years of experience), so he can probably be whatever a director needs him to be at that moment. That Pisces Moon/Venus seems very gentle.
Neptune/Jupiter on the Scorpio Ascendant gives A LOT of presence, as well as that intense Pluto/MC. I think he's up to playing an iconic role.
It'd be interesting to see his synastry with Jenna Louise Coleman (cast mate) , and Stephen Moffat (the show runner), and even the Doctor he grew up watching (was it Baker? I need to check.)
I'm going to check out the transits for when he got the job, and for when he guest-starred on Doctor Who and thought it was a one-time thing