I ride Caltrain daily, but I'd never try to take it arriving on this flight. The trains do not stop frequently at Santa Clara in the evening, even on weekdays. I reckon you'll get to your hotel a few hours sooner if you take the Uber, and that means the difference between getting there at a reasonable hour for dinner vs. after 9pm.

Caltrain is a lot more viable for your return trip, where you can plan ahead, and spending an extra 45 minutes in the lounge on your way home is not nearly as grating as spending 45 minutes waiting alone on a train platform at night when you wish you were at your hotel taking a shower after a long flight. There's plenty of space for luggage on the luggage car, especially if you get on in SF. Do consult the timetable before you go to the station.