Do you get to still enjoy the character's personality because the options you get for dialogue responses match that of their character? Do you still get to play what ever personal quest they have?
Yes and yes. I'd say there is no real downside other than that you don't get to experience as much of that origin character's voice acting because your dialogue choices aren't read out aloud. Other than that there is no reason not to pick an Origin character imo. I highly suggest playing as one.