I've never heard why the choice of a Dart over a Barracuda in '68 and '69. But if you look at a lot of the other Chrysler Corp cars on the show (including cop cars) they were mostly Dodges, not Plymouths.
Perhaps the Dodge Division paid for the placement. Whereas, Plymouth's marketing department might have decided to spend their bucks otherwise...like in drag racing?
Ever notice that when a mafia don, or a corrupt businessman was being tailed by Mannix, the car was usually a dark colored Imperial?
There's an episode with the Dart and a '69 Imperial in it. Photos attached.
I recently bought a '71 Imperial, charcoal metallic with black leather, a true 24,000 mile all-original car. It has a 440 and every option but antilock brakes, which Chrysler pioneered in America.
So, now with the Dart and the Imperial, I can chase my own car around the neighborhood.