About Chopard being "as inhouse as inhouse gets," that only applies to the LUC watches; the other lines like the Mille Miglias are based on the ETA movements. I have a MM GT XL and I'm absolutely impressed with the accuracy ~+1 second a day, so it's not as if it suffers for not having an in house movement.
Back to your question, the Strike One falls under the LUC line, so you'll be safe. You'll get a fantastic Chopard microrotor-based movement.
As for the choice between the Strike One and the Dato . . . well, you're in a win-win situation. No matter what, you'll get a cherishable piece.