Black Cab Tour: Belfast or Derry?

Derry and Belfast are both beautiful - either would be worth a day of your time to explore.
There's probably a little more to see on a Black Cab tour around Belfast but it really comes down to what else you might like to do in either city while you're there. The center of Belfast is pedestrian friendly and of course there's the very worthwhile Titanic Museum. Might add that it was one of the few places where we've ever done a HoHo bus tour, which we enjoyed very much.
Derry is fun to meander around too - especially the circuit around the old city walls. We particularly enjoyed the city museum tucked away near one of the gates beneath the walls, which featured excellent displays showing the long history of the city as well as an exhibit featuring artifacts recovered from one of the 1588 Spanish Armada ships that sank in a bay near Giant's Causeway.
A Black Cab tour around either city would be time well spent if you want a crash course on the history of The Troubles in the company of a knowledgeable local guide.

That's a difficult choice to make. We were in both places last Spring, more time in Belfast than Derry, only did a black cab tour in Belfast. The black cab tour was very educational and worthwhile, but the highlight of Belfast to us was the Titanic museum. We did a tour of the wall in Derry with a very entertaining and informative guide, that spent a good amount of time telling us about The Troubles there, as well as showing us a lot of historical sites. So I guess my answer would be to skip the black cabs, do a guided tour of Derry walls, and squeeze in the Titanic museum later in the day if possible. We so wish we spent more time in Derry.