Whatever the game was coded for. Forcing one to play a game written for the other is generally a fools game.
Not trying to do everything with a single input method makes for far greater control in games, and for many timeless games that would never have worked if forced to use a different input method. Trackballs for Centipede, Missile Command, and Marble Madness. Steering wheels for Super Sprint, Turbo, Spy Hunter. Light Guns for Duck Hunt and Wild Gunman. Twin Joysticks for Robotoron 2084, Battlezone and Smash TV. Paddles for Breakout, Pong, Kaboom, Warlords. Handlebars for Paperboy. Flight Yokes for Star Wars Arcade and Top Gun. The Power PAD for that one game and DDR... R.O.B. for pushing A & B on controller two... Umm.. The Power Glove for... well... that's enough of that. You get the point, moving on...
Kaboom! is a fantastic game that cannot be satisfactorily controlled with either D-pad or Joystick. Same goes for Missile Command and Marble Madness. Sure many games can be controlled with either but they are really only satisfactory with the controller they were designed for. Even Q*bert, which was designed for a joystick, is only properly controllable at home if you hold the controller at a 45 degree angle so even using the proper controller requires a compromise.
That being said, put me down for Joystick.
I have a lot of nostalgia for the joystick. A game like Pac-Man on a proper, short throw, arcade joystick is far more enjoyable than the same exact game on a D-Pad. Even at the height of the NES I would use a Joystick (Beeshu Jazz Stick primarily, liked it better than the Advantage) for arcade games like Contra and the DPad for things like Zelda. A bad joystick is worse than not having one at all though, so quality matters.
If I could only have one, it would be a good joystick, thankfully I have choices.